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THE - yen 
LONDON, EDINBURGH, anp DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


CONDUCTED BY 


SIR ROBERT KANE, LL.D. F.R.S. M.R.LA. F.C.S. 
SIR WILLIAM THOMSON, Knr. LL.D. F.RB.S. &c. 


AND 


WILLIAM FRANCIS, Pu.D. F.L.S. F.R.A.S. F.C.S8. 


‘“Nec aranearum sane textus ideo melior quia ex se fila gignunt, nec noster 
vilior quia ex alienis libamus ut apes.” Just. Lips. Polit. lib.i. cap. 1. Not. 


VOL. VIL—FIFTH SERIES. 
JANUARY—JUNE 1879. Cs. 


LOM DO N:; 
TAYLOR AND FRANCIS, RED LION COURT, FLEET STREET. 


SOLD BY LONGMANS, GREEN, READER, AND DYER; KENT AND CO.; SIMPKIN, MARSHALL 
AND CO.; AND WHITTAKER AND CO. ;—AND BY ADAM AND CHARLES BLACK, 
AND THOMAS CLARK, EDINBURGH ; SMITH AND SON, GLASGOW ;— 
HODGES, FOSTER, AND CO., DUBLIN ;—-PUTNAM, NEW 
YORK ;—AND ASHER AND CO., BERLIN. 


“Meditationis est perscrutari occulta; contemplationis est admirari 
perspicua..... Admiratio generat queestionem, queestio investigationem, 
investigatio inventionem.”—Hugo de S. Victore. 


—‘ Our spirent venti, cur terra dehiscat 

Cur mare turgescat, pelago cur tantus amaror 
Cur caput obscura Phoebus ferrugine condat 
Quid toties diros cogat flagrare cometas ; 

Quid pariat nubes, veniant cur fulmina ccelo, 
Quo micet igne Iris, superos quis conciat orbes 


Tam vario motu.” 
J. B. Pinelli ad Mazonium. 


i 


CONTENTS OF VOL. VII. 


(FIFTH SERIES). 


NUMBER XL.—JANUARY 1879. 


M. W. Beetz on the Excitation of Electricity at the Contact of 
Re remmariane Gases UO. i. CMEC SC A Pa 


UGE Goh See a OS Oe ee ee ee Sena ei 
Mme Hi. Preece on the Electric Light... ee 
Prof. H. F. Weber on the Inductions that occur in the Tele- 

DLS oc te hl eg EAM els eas Ee a 
ME. W. Baily on Starch and Unannealed Glass under the 

Peumecope.s (Plates LaLV:) 60. ie te eee ee 
M. J. Frohlich on a new Proposition in the Theory of Diffrac- 

Moura Nts Applicabion (6. .0 2 Ue ae ke ce 
Mr. W. Crookes on the Illumination of Lines of Molecular 

Pressure, and the Trajectory of Molecules .............. 
Notices respecting New Books :— 

Mr. H. F. Blanford: I. Report on the Administration of 

the Meteorological Department of the Government of 

India in 1876-77; IL. Report on the Meteorology 

of India in 1876; ILI. Indian Meteorological Me- 

PROMS ele OT ate ook, eR UE AA, Be 
Proceedings of the Geological Society :— 

Mr. C. E. Austin on the Distribution of Boulders by other 

Agencies than) that of Icebergs ......02.5.0.00.2-: 

Prof. T. G. Bonney and Mr. F. T. S. Houghton on some 

Mica-Traps from the Kendal and Sedbergh Districts. . 

Mr. W. A. E. Ussher’s Pleistocene Notes on the Cornish 

Coscimmear Padstow eee!) 2 2B OSS Aaa 

Mr. W. A. E. Ussher on the Pleistocene History of Corn- 

parte ek Se ls S Se tah ER a SP 

On the Figure of the Planet Mars. Letter from Professor H. 

Eleminesagyars ore NG CCR ee A eee Ga Le a 
On a new Phenomenon of Static Electricity, by E. Duter .... 
New Observations on the Part played by Pressure in Che- 

mical Phenomena, by M. Berthelot..............0..... 


Page 


15 
29 


34 
39 
ol 
57 


iv CONTENTS OF VOL. VII.—FIFTH SERIES. 


On an Automatic Current-Regulator, by M. Hospitalier .... 
On the Physical State of Central Europe in the Tertiary 
Period, by M. van Tieghem «... 0. 0.0.5.4. 
On the Diffusion of Liquids, by J. Stefan ...... “.. 22a 
On the Specific Heats and Heat of Fusion of Gallium, by M. 
Berthelot wie sak os Meee wis ew Lok ee eee 


NUMBER XLI.—FEBRUARY. 


M. E. Wiedemann’s Investigations on the Nature of Spectra 
Dr. A. Schuster on an easy Method for Adjusting the Colli- 
mator of a Spectroscope. ........ 605. oe. 
Prof. A. M. Mayer on the Morphological Laws of the Confi- 
gurations formed by Magnets floating vertically and sub- 
jected to the Attraction of a superposed Magnet; with 
Notes on some of the Phenomena in Molecular Structure 
which these experiments may serve to explain and illustrate 
Mr. C. V. Boys on a Condenser of Variable Capacity, and a 
Notal-Retlexion Mxperiment) (.),.\. 2:)5.03 (ae 
Mr. J. Brown on the Theory of Voltaic Action............ 
Mr. W. W. Jacques on the Effect of the Motion of the Air 
within an Auditorium upon its Acoustic Qualities...+.... 
Professors J. Perry and W. E. Ayrton on the Music of Colour 
and Visible Motion. (Plates V.and VI.) .............. 
Mr. T. Bayley on Catalysis, and tie Nomenclature of Oxides. . 
Mr. N. 8. Maskelyne on the Crystallography of the Nitroso- 


terpenes of Dr. Tilden. (Plate VII. figs. 1-6.) .......... 


Mr. N.S. Maskelyne on an artificial Diopside Rock formed in 
a Bessemer Converter by Mr. Percy Gilchrist .......... 
Mr. N.S. Maskelyne on Enstatite Rock from South Africa .. 
M. V. von Lang on a Horizontal Goniometer. (Plate VII. 
figs.:7 G8.) scculghi. Hbnd 2a. soe As Oe eee 
Messrs. J. A. Wanklyn and W. J. Cooper on the Moist-Com- 
bustion Process ; some Reactions of Alkaline Permanganate 
OlwRotash? safely cele Stake (isi: eed bean Cate Se oe 
Notices respecting New Books :— 
Mr. G. B. Prescott on the Speaking Telephone, Talking 
Phonograph, and other Novelties.......:.......... 
Proceedings of the Geological Society :— 
Mr. P. Doyle on some Tin-deposits of the Malayan Pe- 
MIMSULA iis wei eis Rewer) Oar GLE ie MRO! i ke 
Mr. J. C. Hawkshaw on the Consolidated Beach at Per- 
WAMPUCOT pryey quel. - “eRe: | ee eee 
Note on Electromagnets in Telegraphy, by Oliver Heaviside . . 
On two new Fluorescent Substances, by E. Lommel........ 
On Thermal Radiation at High Temperatures, by J. L. Soret. . 
On Electrochemical Actions under Pressure, by A. Bouvet .. 


CONTENTS OF VOL. VII.—FIFTH SERIES. v 


NUMBER XLII.—MARCH. 


Page © 
Lord Rayleigh’s Acoustical Observations.—I]. ............ 149 
Dr. J. Hopkinson on High Electrical Resistances .......... 162 


Prof. J. Trowbridge on Methods of Measuring Electric Cur- 
rents of great Strength ; together with a Comparison of the 
Wilde, the Gramme, and the Siemens Machines. (Plate VIII. 

SDS. 1. oh Zo) yas eR Ao leads cea eae area 165 

MM. Kundt and Rontgen on a Proof of the Electromagnetic 
Rotation of the Plane of Polarization of Light in the Vapour 
oxeulphide of Carbon. (Plate VIII. fig. 3.) ....... 00... 173 

Mr. W. J. Lewis on the Analysis of the Rhombohedral System 176 

Prof. Osborne Reynolds on Mr. G. F. Fitzgerald’s Paper “ On 


the Mechanical Theory of Crookes’s Force” ............ 179 
Prof. A. Steinhauser on the Theory of Binaural Audition. 
CT vi5e LLC) eal a ater gia vm eee ne le are er a Ne 181 


Dr. O. J. Lodge on the Determination of the Variation of the 
Thermal Conductivity of Metals with Temperature, by 
means of the permanent Curve of Temperature along a uni- 
form thin Rod heated at one end. (Plate X.)............ 198 

Notices respecting New Books :— 

Dr. Draper’s Scientific Memoirs, being experimental 
Contributions to a Knowledge of Radiant Energy.... 211 
Geological Survey of Canada. Report of Progress for 
we oT oa a PO a ceed Ne Agr DUA 213 
The Rey. W. B. Clarke on the Sedimentary Formations 
Oamibemeontn, Wales 82. Xo. eee eet ease n ss 214 

Proceedings of the Geological Society :— 

Mr. F. Rutley on Community of Structure in Rocks of 
Memmi OA OUN re see se cheng es cage bey Sh woes a anid 215 

Mr. A. Murray on the Distribution of the Serpentine and 
associated Rocks, with their Metallic Ores, in New- 
PCIE ALSNCAO gh tier hence eee RPI ce me ae Ca ernie Riese NER AE 216 

On the Electromagnetic Theory of the Reflection and Refrac- 
tion of Light, by George Francis Fitzgerald, M.A., Fellow 


ieicmigeCollexe: Dublin.) ets ee oe 216 
On the Velocity of very loud Sounds, by William W. Jacques, 

Fellow of the Johns Hopkins University .............. 219 
Researches on Bell’s Telephone, by Henri Dufour ........ 222 
On Harmonic Orbits, by Pliny Earle Chase .............. 224 


NUMBER XUIII.—APRIL. 


Mr. B. H. Cook on the Existence of the Luminiferous Ether.. 225 

Mr. R. D. Oldham on the Modulus of Cohesion of Ice, and its 
bearing on the Theory of Glacial Erosion of Lake-basins .. 240 

Prof. E. Wiedemann on the Luminosity of Gases through 
Necrrica MMinenarmes 22 LO RMT, Es BN a 948 


V1 CONTENTS OF VOL. VII.—FIFTH SERIES. 
Page 
Dr. O. J. Lodge on the Determination of the Variation of the 
Thermal Conductivity of Metals with Temperature, by means 
of the permanent Curve of Temperature along a uniform 
thin Rod heated at one end,..... 5.....:-.....-—: ee 251 
Prof, A. Steinhauser on the Theory of Binaural Audition.... 261 
Mr. N. D. C. Hodges on a new Absolute Galvanometer .... 274 
Professors W. E. Ayrton and J. Perry on a new Determina- 
tion of the Ratio of the Electromagnetic to the Electro- 
static Unit of Electric Quantity. (Plate XI.) .......... 277 
Notices respecting New Books :— 
Mr, F. Rutley on the Study of Rocks, an Elementary 


Text-book on Petrology ........ ihe 3, selene 289 
Annual Report of the Department of Mines, New South 
Wales, for the year 1877 ...... eee .. - 290 


Proceedings of the Geological Society :—_ 
Messrs. Strahan and Walker on the Occurrence of Pebbles 
with Upper-Ludlow Fossils in the Lower Carboniferous 


Conglomerates of North Wales. .......2 3255 aee 291 
Dr. H. Hicks on a New Group of Pre-Cambrian Rocks 
(the Arvonian) in Pembrokeshire ..... 3...) 24 4qee 292 


Dr. H. Hicks on the Pre-Cambrian (Dimetian, Arvonian, 
and Pebidian) Rocks of Caernarvonshire and Anglesey 293 
Prof. T. G. Bonney on the Quartz-felsite and associated 
Rocks at the base of the Cambrian Series in North- 
western Caernarvonshire ... ...... «204+ 02 ee 293 
Messrs. Bonney and Houghton on the Metamorphic 
Series between Twt Hill, Caernarvon, and Port Di- 


TAGE WUC a cook wake aay c. ye oi doe oe ojo voles epee eee er 294 
Mr. F. Rutley on Perlitic and Spherulitic Structures in 
the Lavas of the Glyder Fawr, North Wales........ 294 
Mr. H. 8. Poole on the Gold-leads of Nova Scotia .... 295 
On the Diffusion of Liquids, by J. Stefan ................ 295 


On the Spectrum of Oxygen, and on the Electrical Luminous 
Phenomena of Rarefied Gases in Tubes with Liquid Elec- 
trodes, by M..Paalzow ........4......25- ea 297 


NUMBER XLIV.—MAY. 


Dr. G. Quincke on the Formation of Emulsions, and the Ac- 

tion of the Bilean Digestion ~ 24.20... =. 301 
Capt. W. de W. Abney on the Photographic Method of Re- 

gistering Absorption-Spectra, and its Application to Solar 

Physies ses ects he Fe ee ee 313 
Dr. A. Schuster on Spectra of Iughtuime | ..4). +. = eee 316 
Mr. J. W. L. Glaisher on a Property of Vulgar Fractions .. 321 
Mr. R. 8. Brough on the proper Relative Sectional Areas for 

Copper and Iron Lightming-Rods........5.5..0.058-06= 336 
Mr. D. J. Blaikley’s Experiments for determining the Correc- 

tion to be added to the Length of a Cylindrical Resonant 


CONTENTS OF VOL. VII.——FIFTH SERIES. vil 


Pa 
Tube to find the true Wave-length, and the Velocity of 


PesOmeROtb STN UMUC Se ge ge Pon oe er tyes 5 oa bag oo ness 339 
Prof. P. G. Tait on the Dissipation of Energy ............ 344 
Sir W. Thomson on Thermodynamic Motivity ............ 348 
Dr. C. W. Siemens on the Transmission and Distribution of 

Energy by the Electric Current. (Plate XII:) .......... Jdo2 
Messrs. Wanklyn and Cooper on the Products of the Oxida- 

tion of Wool—Cyano-propionic Acid .................. 306 


Notices respecting New Books :— 
M. A. Terquem’s Sur les Courbes dues 4 la Combinaison 
de deux Mouvements vibratoires perpendiculaires .... 365 
_ American Journal of Mathematics, Pure and Applied .. 366 
Proceedings of the Geological Society :— 
Mr. D. Mackintosh on the Directions and Limits of Dis- 
persion, Mode of Occurrence, and Relation to Drift- 
deposits of the Erratic Blocks or Boulders of the West 


ovrmeland and Hast of Wales... 02.2... -. see. 367 
Messrs. Peach and Horne on the Glaciation of the Shet- 
Pemideslccger Cte et Sat cod Sin ee ot ths ot. Ld das 367 
Mr. A.J.Jukes-Browne on the Southerly Extension of the 
Hessle Boulder-clay in Lincolnshire .............. 368 
Prof. EH. Hull on the Geological Age of the “‘ Dingle Beds ” 
pipeeeeeMOamiin CEUs 2) i ois. 14: Meg eavde mele san eke oe 368 


Mr. W. J. Sollas on some Three-toed Footprints from the 
Triassic Conglomerate of South Wales, and on the Silu- 


rian District of Rhymney and Pen-y-lan, Cardiff .... 369 
On the Optical Properties of Starch, by Viktor v. Lang .... 370 
On the Magnetic Rotatory Power of Vapours, by E. Bichat.. 371 
On an Electrical Burner and Blowpipe, by M. Jamin ...... 372 
On the Electrical Perforation of Glass, by Prof. A. von Walten- 
(| L RESID ‘DRG po Re ree ee ey a ac Olt ene a dea 374 


On the Pressures exerted by Galvanic Deposits, by M. Bouty.. 375 
New Estimate of the Sun’s Distance, by Pliny Earle Chase, LL.D. 377 
Contribution to the Theory of the Microphone, by Hermann 


22IUQTE, Ug sige 5 cans gana est a eth ee a Rs Rae tae a O77 
On the Variation of the Thermal Conductivity of Metals with 
Gemperature, by Oliver... Lodge. .).45)koae es eee ah 380 


NUMBER XLV.—JUNE. 


Mr. O. Fisher on the Thermal Conditions and on the Stratifi- 
earonsouure samiacetic’ Lent Te PSs ee eG Cee a 381 
Dr. A. R. Leeds on the Action of Light upon the Soluble 
Todides, with the Outlines of a New Method in Actinometry 393 
Professors J. Perry and W. E. Ayrton on a new Theory of 
Homrestiau! Masmehsms:.. 5. .cu aan lt ele oes vie es ok 401 
Mr. F. D. Brown on the Maintenance of Constant Pressures 
and “eniperaimmess (Plate ATE) (a... eek oe ee ws 411 


Vill CONTENTS OF VOL. VII.—FIFTH SERIES. 
Page 
M. A. Naquet’s Considerations on the two Memoirs of Sir B. : 
C. Brodie on the Calculus of Chemical Operations........ 418 
Prof. G. Van der Mensbrugghe on a new Application of the 
Potential Energy of Liquid Surfaces .................. 432 
Dr.E. J. Mills on the Detached Colorimeter, and on Colorimetry 437 
Proceedings of the Geological Society :— 


Mr. J. A. Phillips on the History of Mineral Veins .... 441 

Mr. N. Taylor on the Cudgegong Diamond-field, New 
South Wales. 1.5. Gin sas «4 ae alone onenee ce ee rr 442 

Note on the Magnetic Effect of Electric Convection, by H. A. 
Howland (is wes s woe ne he eee eo er 442 
On Electric Boundary Layers, by Prof. Helmholtz ........ 443 


A Theoretic and Experimental Demonstration of the definition, 
“The Temperature of a Body is represented by the Length 


of the Thermal Oscillation of its Molecules,” by R. Pictet.. 445 


On Ozone and the Electric Effluvium, by M. Berthelot...... 447 


PLATES. 


I., I., II., IV. Illustrative of Mr. W. Baily’s Paper on Starch and 
Unannealed Glass under the Polariscope. 


V., VI. Illustrative of Professors Perry and Ayrton’s Paper on the 
Music of Colour and Visible Motion. 

VII. Illustrative of Prof. N.S. Maskelyne’s Paper on the Crystallo- 
graphy of Nitrosoterpenes, and M. v. Lang’s on a Horizontal 
Goniometer. 

VIII. Illustrative of Prof. J. Trowbridge’s Paper on Methods of 
Measuring Electric Currents of great Strength, and MM. Kundt 
and Rontgen’s on the Electromagnetic Rotation of the Plane of 
Polarization of Light in the Vapour of Sulphide of Carbon. 

IX. [lustrative of Prof. A. Steinhauser’s Paper on Binaural Audition. 

X. Illustrative of Dr. O. J. Lodge’s Paper on the Determination of 
the Variation of the Thermal Conductivity of Metals with Tem- 
perature. 

XI. Illustrative of Professors Ayrton and Perry’s Paper on a new 
Determination of the Ratio of the Electromagnetic to the Elec- 
trostatic Unit of Electric Quantity. 


XII. Illustrative of Dr. C. W. Siemens’s Paper on the Transmission 
and Distribution of Energy by the Electric Current. 


XIII, Illustrative of Mr. F. D. Brown’s Paper on the Maintenance of 
Constant Pressures and Temperatures. 


ERRATUM IN VOL. VI. 
Page 457, 15 lines from bottom, for ‘006 read 60 


ERRATA IN VOL. VII. 
Page 43, line 17 from top, for at read as 
— 43, — 5 from bottom, for Putting =0 read Putting «=0 
— 45,— 3 + for value read values 
— 47, — 2 os for tan read tan 2e 


ee 


eres Oe ee eee 


LIL 


LONDON, EDINBURGH, ayn DUBLIN 


PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES.] 


SANTA Y 18%9, 


Gases. By W. Buerz*. 


| * Translated from Wiedemann’s Annalen, 1878, No. 9, vol. v. pp. 1-20. 
| tT Pogg. Ann. vol. xxvii. p. 505. {t<Phl Trans, 1813, pt. 2, p. 97. 
§ Comptes Rendus, t. lxiv. p. 364 (1867). 


Phil, Mag. 8. 5. Vol. 7. No. 40. Jan. 1879. B 


_——— 


—- ——— 


I. On the Excitation of Electricity at the Contact of Solids and 


Da publishing my first experiments on the electro- 

motive forces of gas batteries, I expressed my ideas re- 
specting the place at which the seat of the difference of tension 
| produced was to be soughtt. Grove had assumed that it was 
| the place of contact of the platinum, gas, and liquid{. I did 
not admit the universal correctness of that assumption: it is 
certainly not true for gases which, like chlorine, strongly ab- 
| sorb water; for a platinum plate entirely immersed in a liquid 
containing chlorine behaves, in respect of its electricity, very 
differently from a plate of platinum immersed in a liquid free 
from chlorine. I showed that what happens with other gases 
may be regarded as precisely similar; only it is the less di- 
stinctly manifested the less soluble they are in the liquid. 
The upper part of a platinum plate, enveloped in hydrogen, I 
covered with an insulating layer, so that the free platinum 
was entirely covered by the liquid, and yet it preserved a real 
gaseous element, certainly of somewhat less electromotive 
force than if the upper end of the platinum had been directly 
surrounded by the gas. I have in the place above cited given 
my views respecting the reasons for this difference. Gaugain 
subsequently arrived at the conclusion that the platinum acts 
\ only upon the gases dissolved in the liquid§. A platinum 


2 M. W. Beetz on the Excitation. of Electricity 


wire surrounded by the gas.and dipping in the liquid he gra- 
dually lowered until it was all covered by the latter; he then 
obtained precisely the same difference of tension as when one 
part of the wire was surrounded by the gas and the other by 
the liquid. This result I accounted for by remarking that, in 
making the experiment thus, the wire had at first been actu- 
ally in contact with the gas, and then carried a condensed 
layer of gas with it into the liquid*. I have further, in the 
above-mentioned treatises, stated my views upon the follow- 
‘ing :—that the amount of the difference of tension between a 


clean metal and one coated with a gas depends on the degree © 


- of such condensation of the gases; that the condensation 1s 
greater or less, according to the metal with which the gas 
elements have been produced; and that a singularly high 
degree of condensation is preduced by electrolytic polariza- 
tion, on account of which the electromotive force of the gases 
is in this case peculiarly great. The considerable difference 
of tension produced by the action of even small quantities of 
hydrogen on platinum I compared to the analogous pheno- 
menon shown by the position of the amalgams in the ten- 
sion series. Macaluso has moreover pointed out that far 
greater electromotive forces can be generated by the long- 
continued electrolytic evolution of hydrogen, or chlorine, or 
at platinum or carbon electrodes than by simple contact of 
the gases with the plates or by gas being evolved at them 
during a short time; he therefore believed that an active 
state must be ascribed to the gases separated by electro- 
lysis, similar to that which is known to us in oxygen{. In 
truth, as regards hydrogen, the presence of an active modifi- 
cation, previously assumed by Osann, has been rendered very 
doubtful by Magnus f. 

While the subject of all the above investigations was the 
presence of considerable quantities of gas on the metal plates, 
there has recently been a discussion in detail of the case in 


which only thin films of gas have formed upon the plates. » 


FE. Kohlrausch has subjected these films to a careful consi- 
deration§; and Helmholtz|| and Herwig{] have made the 
analogy between a layer of liquid connecting two polarized 
electrodes and a condenser the subject of their investigations. 
Herein Helmholtz has advocated the view that in the polari- 


* Pogo. Ann. vol. cxxxii. p. 461. 

+ Ber. d. k. stichs. Ges. d. Wiss., math.-phys. Cl. 1878, p. 306. 
t Conf. Wiedemann, Galvanismus, 2nd ed. vol. 1. p. 538, 

§ Gott. Nachr. ¥872, No. 23, p. 453. 

|| Monatsb. d. Berl. Ahad. d. Wiss. 1878, p. 587. 

4 Wied. Ann. i1. p. 566, 


ee ee ae Se 


at the Contact of Solids and Gases. 3 


zation not merely portions of gas adhering to the surface, but 
also portions which have penetrated deeper into the platinum 
must play a part—the possibility of which had been already 
indicated by Graham’s experiments on palladium and plati- 
num. In fact, Crova*, and after him Root also}, succeeded 
in proving that, with the electrolysis of dilute sulphuric acid, 
hydrogen penetrates through a platinum plate, since the plate 
not only exhibited polarization on the side where the electro- 
lysis took place, but was protected on the opposite side from 
_ all electrolytic action. 

But few investigators, in studying galvanic polarization, 
have taken into consideration other gases than hydrogen and 
oxygen; hence the question arises whether the views which 
hold good for these two gases, and preferably for hydrogen, 
can be extended in their entirety to all cases of polarization. 
A series of experiments which I have made with palladium 
and carbon electrodes may contribute to the answering of this 
question. 

To procure exact knowledge respecting the electromotive 
position of palladium is a very difficult task. Palladium as 
obtained in commerce has always been heated to incandes- 
cence, and has taken in gases in the process, as Graham has 
shown. The means usually employed to expel such occluded 
gases, especially hydrogen, from the palladium are so far suffi- 
cient that chemical analysis can show no traces remaining, 
but do not suffice to destroy all change in the electromotive 
state of the metal. This is especially true of the treatment 
with the mercury air-pump ; I have never been able in this 
way to bring back a palladium plate quite to its previous 
electromotive position after evolution of hydrogen had taken 
place on it. On the other hand, the last trace of hydrogen 
can be completely removed by a long-continued evolution of 
oxygen. But then the plate becomes covered with a coat of 
brown oxide; and if this be ever so carefully rubbed off, yet 
the plate always takes a much more negative position in the 
tension series than if it had been cleaned with hydrochloric 
acid. For the determination of that position I made use of 
my universal compensator{, with which also all the other 
measurements of the differences of tension we shall have to 
consider were made. The palladium plate to be tried dipped 
into very dilute sulphuric acid (1: 100), and thus formed the 
negative constituent of an element, of which the positive con- 
sisted of an amalgamated zinc cylinder standing in a concen- 

* Mondes T. V. p. 210 (1864); Wied. Galv. (2) i. § 498. 


+t Monatsber, d. Berl. Akad. d. Wiss. 1876, p. 217. 
f Wied. Ann. ii. pols”: 
B2 


4 M. W. Beetz on the Excitation of Electricity 


trated solution of sulphate of zinc. The two fluids were con-- 


nected with one another by means of a siphon filled with 
dilute sulphuric acid and closed at both ends by clay cells. 
A Daniell element in the form previously employed by me 
served as unit, its zinc-cell being filled with solution of sul- 
phate of zinc. If d denote electromotive force of such an 
element, and D that of a Daniell element the zinc-cell of 
which contains dilute sulphuric acid, then d2=0:95D. As the 
force D is generally taken for the unit force, I have reduced 
all the following data to the same. In like manner I cite 
from previous memoirs the values of the electromotive forces 
in terms of the unit D=1. I also regard alwaysas the point 
of issue, 7. e. the positive part of the element in question, the 
amalgamated zinc in dilute sulphuric acid; so that, for ex- 
ample, the electromotive force of zinc in dilute sulphuric 
acid | Platinum in dilute sulphuric acid (or, abbreviated, 
Zn | Pt)=1:61D; Zinc in dilute sulphuric acid | Platinum 
coated with hydrogen in dilute sulphuric acid (or Zn | Pt, H) 
=0°80D, &. Thus I found the force Zn | Pd, when I had 
only mechanically rubbed the oxidized plate, always very 
great, varying between 1°90 and 2:03D, evidently because 


there were always some remains of oxide still adhermg. But. 


if the brown oxide was removed by diluted hydrochloric acid, 
the electromotive force was found to be constant within tolerably 
narrow limits—namely, 


I-24 26, 124 1-29, 132) ee 
Mean ... Zn | Pd=1°28 D. 


If we may regard as actually pure the palladium thus 
cleaned, its position in the electromotive series is considerably 
nearer to zinc than that of platinum. Still it is not advisable, 
in measuring-experiments, to refer the position of a palladium 
plate polarized by any gas to that of pure palladium; it can 
be much more certainly ascertained if under all circumstances 
the amalgamated zinc plate in a concentrated solution of sul- 
phate of zine be united with the plate to be examined by the 
siphon to form a series, or if two plates polarized by different 
gases be placed immediately opposite one another. 

Two strips cut from the same sheet of palladium were 
passed through corks which closed the upper ends of two 
glass tubes. The tubes were filled with diluted sulphuric 
acid and plunged upside down into a glass containing the 
same fluid. Oxygen was then introduced into one of the 
tubes, and hydrogen into the other. Both the gases had been 
evolved by electrolysis and kept in small gasometers, from 
which they could be taken as required. 


at the Contact of Solids and Gases. 5 


The plate enveloped in oxygen exhibited not the slightest 
alteration in its electromotive quality, neither immediately 
nor after a longer-continued action of the oxygen. The dif- 
ference of tension Zn | Pd, O was invariably the same as 
Zn | Pd. The hydrogen gas, on the contrary, exerted a 
powerful influence from the first moment onwards: at the 
appearance of the first gas-bubble the palladium became at 
once positive; and after gas had been absorbed for some time 
by the metal the force Zn | Pd, H was found, in different ex- 
periments made with plates or wires, to be 

CGE 0095 OFC 0-102 O60: 
Mean ...' Zn | Pd; H=0°69 D. 


At this height it remained even when hydrogen had been in- 
troduced from without (or evolved on the plate itself) so long 
that the palladium could absorb no more, but free hydrogen 
enveloped its upper surface. According to this, the tension- 
difference would be 

Pd,.H | Pd=1:28—0°69=0°59 D, 
while I had previously found 

Pt |p Pt=0°3lD. 
Whether the palladium was employed bright, or coated with 
palladium-black, made no difference. . 

Further, palladium plates were used as the electrodes of a 
Grove’s pile of three or four couples, or a Meidinger’s pile of 
six couples. These electrodes were also enclosed in glass 
tubes, to enable me to continue the electrolysis until the hy- 
drogen was no longer absorbed by the palladium. The mea- 
surement of the polarization present was, as before, effected 
by means of the universal compensator ; with some practice 
the simple discharge obtained at it furnished very constant 
results, even though, like all similar contrivances, it was not 
entirely free from the inconvenience that the polarization- 
current was not closed till some, although a very short, time 
after the interruption of the polarizing current. To distin- 
guish it from the electromotive force Zn | Pd, H, which was 
excited by merely enveloping a palladium plate in hydrogen, 
I denote by Zn | Pdy the force excited by the galvanic polari- 
zation of hydrogen. This was found to be 


O69. UC * Or6r 
Mean ... Zn | Pdy=0°69 D,— 


that is, exactly equal to Zn | Pd, H. In this case, therefore, 
no more hydrogen could be pressed into the palladium plate ; 
the plate was already saturated with hydrogen. | 


6 M. W. Beetz on the Excitation of Electricity 


Measurements executed with the positive electrode gave 
indefinite results. The plates immediately became brown and 
strongly negative, so that I obtained for the force Zn | Pdo 
values like 2:12 D. In correspondence with this, for the total 
polarization Pdy | Pdg very great forces were found; but I 
convinced myself that their numerical evaluation was of no 
importance, since here not the action of gaseous active or 
passive oxygen comes into consideration, but that of the de- 
posited layer of oxide. On this account, of the numerical 
data obtained by other observers on the strength of the pola- 
rization on palladium plates, I, can only compare one with 
my own results: Graham*, namely, found: that the polariza- 
tion produced by from 1 to 4 Bunsen elements was 


Pd. | Fd 150-35 D: 
I find, on electrolysis by 4 Grove or 6 Meidinger, 
1:83, 1:77, 
Mean «../ Pd, | Pt,— 130 D; 


therefore very nearly the same as Graham; but the platinum 


plate was not polarized to the maximum. A statement made 


by Pearnell{, according to which the polarization 
Pd, «| Pdg=0°306 D, 


is evidently much too low. 

Covering palladium with palladium-black made no alteration 
in the polarization by hydrogen. Boéttgert gives proofs of the 
powerful polarization of such blackened palladium plates; but 
the prominent action comes into consideration only when the 
closing of the current is continued, while with the momentary 
closing required by the compensation method it is of no im- 
portance. The palladium-black covering the positive electrode 
is immediately pushed off; the layer of oxide which forms 
completely exfoliates the black coating. 

Of other gases, I have caused chlorine, carbonic oxide, ethy- 
lene, and sulphuretted hydrogen to act upon palladium. 

The action of chlorine commences with the first traces that 
enter the fluid and are absorbed by it, and is strongly nega- 
tive. When the fluid was saturated with chlorine there ap- 
peared the electromotive force 


Zn | Pd, Cl=2-04D; 
on the combination standing longer, the force certainly con- 


* Phil. Mag. [IV.] xxxviii. p. 243. 
+ Ibid. xxxix, p. 52. { Jahresber. d. Frankf. ph, Ver. 1875-76, p. 23, 


— sca eatin \ 


! 

| 
} 
| 
i 
| 
. 


: 


ee a ae 


at the Contact of Solids and Gases.” 7 


tinued to rise, but only slightly. Accordingly 
ede | ice Cl=- 0:76). 


The attempt to polarize palladium with chlorine by electro- 
lysis of hydrochloric acid had to be given up as useless. Even 
chlorine gas introduced from without into the gas element 
attacked the palladium and browned both the metal and the 
liquid after a time; while in the electrolysis the attack com- 


menced immediately and with violence, and a coating of pal- 


ladium-black was at once driven off. 

Hthylene and carbonic oxide gas, into which the tube con- 
taining a palladium plate was introduced, polarized it positively: 
indeed, after introducing the ethylene, I found the values 

1:29,) 1:24, 523, 
Mean’... An’) Pd, C,H, = 123 D5 


and after the introduction of the carbonic oxide, 


1 OS. TG: 
Mean ... Zn | Pd, CO=1-05 D. 


‘Therefore 


Pd, C, 0, | Pd =0-05D, 
Pd, CO | Pd=0-23D. 


When sulphuretted hydrogen was brought into the tube, I 
obtained immediately after the appearance of the first bubble 
the tension-difference 


Zn | Pd, H, 8 =0°88 D. 


On continually agitating the liquid with fresh quantities of 
gas until it was saturated, the above difference was scarcely 
altered ; after two successive fresh saturations I obtained 


0:87 and 0°87; 
so that we have 
Pd, H,8 | Pd =0-41D. 


The carbons with which I have experimented were four- 
edged rods of retort-carbon, such as are used for electric lamps. 
They are of great hardness and very close structure. They were 
purified by boiling in nitric acid, in water, and lastly in dilute 
sulphuric acid, in which they were then left to cool. If they 
were to be used in dilute hydrochloric instead of sulphuric 
acid, this liquid was then the last in which they were boiled. 


‘Through this treatment the rods were pretty homogeneous. 


Introducing them into dilute sulphuric acid, and uniting this 


by the siphon with the zinc-cell, 1 obtained the following elec- 


8 M. W. Beetz on the Excitation of Electricity 


tromotive forces :— 


1:32 .1:33. 1°28: 1°30 30 ~ aeae 
P27 1:27: 1:38" Pare are Miles 


Mean ... Zo |;0.— trai), 


For each series of experiments fresh carbons had to be em- 
ployed, as the carbons, altered by the various actions which 
they had undergone, could not be again brought into their 
initial condition. Oxygen or hydrogen, led into the tubes 
enclosing the carbons, produced not the slightest result; the 
electromotive force of the combination remained quite unal- 
tered = Zn | C. The behaviour of carbonic oxide and ethy- 
lene gas was just as indifferent. These results do not accord 
with my earlier experiences, according to which the gases 
mentioned acted as electromotors on Bunsen’s carbon also, and 
by which I was induced to assume that the electromotive 
forces of carbun batteries composed of different metal (or car- 
bon) plates, but of the same gases, stood in a definite relation, 
dependent on the condensing force exerted by the metals upon 
the gases. The carbons with which I worked thirty years 
since were very porous—battery carbons prepared from coke 
and coal; and at that time I said that the coefficient of con- 
densation which I found for my carbons was certainly not to 
be regarded as holding good generally, but that other carbons 
might behave differently. Thus, with those now used such 
proportionality is altogether out of the question; the gases 
employed cannot have undergone any condensation upon the 
carbon. In order to test this rather unlikely fact more mi- 
nutely, I cut out of such retort-carbon two regular-shaped pieces, 
each of 0°5 x 0°5 centim. cross section and 1 centim. length, 
the solid content of each being thus 0:25 cub. centim. These 
pieces were strongly heated and then introduced into ammonia 

as which was enclosed in measuring-tubes over mercury. 
After the old temperature was fully restored, the volume of the 
ammonia gas had increased by a minute quantity which could 
not be precisely determined with the altered form of the me- 
niscus. Had the increase amounted to 0°25 cub. centim., it 
would have been a proof that in fact no gas was absorbed; 
still the experiments showed that the retort-carbon had taken 
up as good as none of even this gas, which is briskly absorbed 
by the other sorts of carbon. 

Very different was the behaviour of the carbon to chlorine. 
This gas was conducted into the tube of the element until it 
was no longer completely absorbed ; then the connexion of the 
conducting liquid with the zinc-cell was restored, when the 


aun eT Ce ee ee ee 


——aee 


at the Contact of Solids and Gases. 9 


following tension-differences were found :— 
eieralson,. 194, 201, 
Miean..'7a |.C,-Cl — 0:69 D; 
from which it follows that 
Cre: CL t-6o wp: 
When the chlorine was not brought into the tube from 
without, but evolved immediately at the carbon electrode by 


electrolysis of diluted hydrochloric acid, still greater electro- 
motive forces were obtained—namely, 


2135: 27253) 72518, 
Mean ... Zn | Cq=2°19 D. 


With longer-continued polarization Macaluso observed yet 
higher values. 

That carbon electrodes are strongly polarized by electrolysis 
in dilute sulphuric acid is already known; Dufour’, particu- 
larly, has recently called attention to it. I found the polari- 
zation for both electrodes together 


ZOSst 122 we Ic O 0. cer. 
Mean ... O,, | C,=2°07D. 


After restoration of the connexion with the zinc-cell, there 
was found for the polarization of the negative electrode— 


0:27, 0:26, 
Mean ... Zn | C,,=0°26D; 
and for the positive— 
ZUG) (2°38, 
Mean... Zn | Co=2°27D. 


Further, by direct comparison were found :—the force be- 
tween pure carbon and carbon polarized with hydrogen— 


1:07, 1-11, 
Mean, ...1C1|'C— 1:09); 


and between carbon pure and polarized with oxygen— 


POG 104, 
Mean... € );Cg=1-05 D. 
Hence we should have 
Cot Coal LD, 
while 2°07 had been found directly. 


ae Soc. Vaud. [2] xix. p. 68 (1876); Wied. Ann. Beiblitter, i. 
p. 573. 


10 M. W. Beetz on the Excitation of Electricity 


When the carbon electrodes at which the electrolysis had 
taken place were left in position, their difference of tension in 


comparison with pure carbon diminished only slowly and im- 


perfectly. The carbon at which hydrogen had been evolved 
showed still, after twenty-four hours, tension-differences 
against pure carbon amounting to about 0:6 D, while that at 
which oxygen had been evolved showed about 0°3D. LHvyi- 
dently, however, further chemical changes had taken place in 
the carbons:—in the negative, probably reductions of metallic 
oxides mixed with it in spite of all the purification it had un- 
dergone; in the positive, conversely, oxidations. An electro- 
lysis, between carbon electrodes, of dilute sulphuric acid 
delivered, during the same time in which at platinum elec- 
trodes 27°36 cubic centims. of hydrogen were separated by 
the same current, 26°86 cubic centims. of hydrogen, but only 
1°71 cubic centim. of oxygen. Tor the reduction, therefore, 
but very little hydrogen was consumed, and so much the more 
oxygen for the oxidation; indeed it was the carbon itself that 
was oxidized, forming carbonic acid and carbonic: oxide gas. 
When, as in the present experiments, small quantities of gas 
are separated from large masses of conducting liquid, the car- 
bonic acid is all absorbed; but if by long-continued electro- 
lysis of a neutral-salt solution (for instance, Glauber salt) 
larger quantities of gas are evolved, the gas which collects 
above the liquid contains considerable amounts of free carbonic 
acid, which can be removed by agitation with caustic potash. 
The remaining gas proves to be carbonic oxide. The propor- 
tion of the two gases to one another appears to depend on the 
density of the current*. At the same time the carbon anode 
is violently attacked and carbon powder copiously thrown off 
from it, like the palladium dust thrown off from the oxidizing 
palladium plate; while the surface of the carbon becomes 
coloured deep blue. Macaluso has also observed this destruc- 
tion of the carbon with the evolution of chlorine at a carbon 
electrode. 

Different again, lastly, was the behaviour of carbon to sul- 
phuric acid. After a few gas-bubbles had made their appear- 
ance at the carbon (just as before with palladium), no change 
was shown in its electromotive position. As the diluted sul- 
phuric acid was repeatedly shaken with fresh quantities of 


* Tn consequence of the complete disappearance of the gas in my first 
experiments, I at first thought that the carbon itself was not oxidized at 
all. An incidental communication from M. Laurent, Ingenieur, of Bel- 
fort, who had observed the occurrence of carbonic oxide and acid on elec- 
_trolysis at carbon electrodes, induced me to repeat my experiments on a 
larger scale. I intend to carry them on still further. 


at the Contact of Solids and Gases. 11 


sulphuretted hydrogen the carbon continually approached 


nearer to the positive end of the tension-series; there were 
observed, namely, for Zn | C, H, 8 :— 


At the commencement... 1°29 
After the second saturation . . 1:13 
After the third y me teen be U3 
After the fourth , ah aye Phe 


Thus, with the saturation of the solution, the electromotive 
force approached towards a limiting value which is to be set 
down as about 

Zn | C, H,S=1:02 D. 
so that 
C, H,8 | C becomes =0°29 D. 


The electromotive forces which were called forth at the pal- 
ladium by hydrogen, sulphuretted hydrogen, carbonic oxide, 
and ethylene show, in fact, again a similar proportionality, as 
I had previously conjectured for all the metals. In the fol- 
lowing Table I place side by side the values before found. for 
platinum and those now found for palladium, and calculate 
from the forces observed at platinum those to be expected at 
palladium, by multiplying the former with the ratio 


Pd | Pd, H: Pt | Pt, H=0-59 : 0-81=0°73. 


Pi, Pd. Pd. 
Found. Found. Calculated. 
Boe es Orel 0°59 0:59 
Ah ae a 0°42 0°50 
eee Sy ke IG 35 0:20 
Met co. Oe 0:05 0-04 
Sens oO ) 0) 


For the retort-carbon, on the contrary, nothing similar is to 
be observed ; its state was in general changed only under the 
influence of greater solubility of the gases or the electric polari- 
zation. Besides we have no longer any right to designate the 
factor 0°73 as the coefficient of condensation for palladium, 
since we know that palladium condenses hydrogen much more 
strongly than platinum does. 

From the results obtained the following is now evident :— 
Platinum, palladium, and carbon behave to chlorine exactly 
alike, so much so that the numerical values found for the 
electromotive forces Zn-| Pt,Cl; Zn | Pd,Cl; Zn | ©, Cl 
stand very near to one another; they amount to 2-08, 2-04, 
1:97 D respectively. The values which were obtained on the 
electrolytic evolution of chlorine are here left out of considera- 
tion, because the attack which therein took place on the elec- 


12 M. W. Beetz on the Hxcttation of Electricity 


trodes makes the comparison unsafe. The almost perfect 
agreement between Pt, Cl and C, Cl was also remarked by 
Macaluso*. It looks as if the plate dipping in the chlorine 
solution served solely as a conductor; and in fact we cannot 
here speak of the electromotive force excited by a gas, but 
have simply to do with the electromotive action of a liquid, 
which increases with the degree of concentration of the liquid. 

The solubility of sulphuretted hydrogen in water is similar 
to that of chlorine ; but it behaves otherwise to platinum and 
palladium than to retort-carbon. The latter, again, occurs 
only as a body immersed in a solution, by which it is the more 
intensely electrically excited the more concentrated the solu- 
tion. Platinum and palladium are already strongly excited by 
the first quantities of gas; they evidently draw it from the 
liquid to condense it in or upon themselves. 

The rest of the gases which have been taken into considera- 
tion are but little soluble in water. Of course, in the usual 
form of the gas battery, something even of these must at first 
be dissolved in the conducting liquid in order to become 
active ; but the quantity is too inconsiderable to cause the so- 
lution to act on the conducting plate essentially otherwise 
than the liquid which has absorbed no gas at all. In these 
cases something else must come into play to generate a differ- 
ence of tension—namely, either an affinity (or, generally, an 
action of molecular forces by which the gases incorporate 
themselves with the metal plate), or the action of an electro- 
lyzing current which either drives the gases into the metal or 
condenses them upon its surface. On palladium hydrogen 
exhibits this penetration in the highest degree, on platinum 
in a less degree, on retort-carbon not at all. The aid of gal- 
vanic polarization is superfluous with palladium, useful with 
platinum, absolutely necessary with retort-carbon to generate 
a difference of tension. Carbonic oxide and ethylene act in 
the same manner as hydrogen, but far more feebly. If we 
could condense them by galvanic polarization, it would in all 
three cases be useful; with carbon, indeed, it would be indis- 
pensable. Sulphuretted hydrogen stands, with reference to 
its behaviour to platinum and palladium, near to hydrogen, 

and near chlorine in consequence of its solubility. 

I made an experiment to ascertain if chlorine, which so 
readily attacks the surface of metals, penetrates also into or 
through them. LHxactly as in Root’s experiment, two glass 
vessels were cemented to the two sides of a much broader 
sheet of palladium b. Both vessels were filled with diluted 
hydrochloric acid; and palladium electrodes a and ¢ dipped 


* Loe. cit. p. 362, . 


ee Se 


< tts 


at the Contact of Solids and Gases. 13 


into them. Between a and 6 a current was closed, so that 
chlorine was evolved upon the side of 6 turned towards a. 
On the other hand, 6 and ¢ could be connected with the gal- 
vanometer by momentary closings. To my astonishment, 
after a time there was shown an electric difference in which, 


not b, but ¢ appeared negative. Of the liberated chlorine, 


traces passed through the atmosphere to the surface of the 
liquid in the other vessel, and through it arrived at the elec- 
trode c. That slight traces of chlorine act at once electromo- 
tively on platinum also had already been remarked by Maca- 
luso; and Iam now of opinion that the oxygen gas which I 
used for my first measurements on gas batteries, and which 
had been prepared from chlorate of potass, always carried 
withit traces of chlorine, although I thought I had sufficiently 
purified it by washing; for with oxygen obtained by electro- 
lysis I could as little excite platinum electromotively as palla- 
dium. I now altered my apparatus by giving it the form of a 
U-shaped tube, the horizontal part of which, 80 centims. long, 
was divided in the middle by a thin plate of palladium into 
two halves. I first filled both sides with diluted sulphuric 
acid, and evolved hydrogen at the side of 6 facing the plate a, 
and that by closing the circuit for only a few seconds. The 
action of hydrogen that had penetrated through the palladium 
was very soon perceptible: the plate b also became positive on 
its reverse side. The experiment cannot be long continued ; 
for the plate bends so much that it soon breaks loose from 
its attachment. A fresh tube was now filled with diluted 
hydrochloric acid. The long layer of liquid permitted none 
of the evolved chlorine to escape, while the electrode c re- 
mained perfectly indifferent until the plate 6 was eaten quite 
through. In order to fix more exactly the instant at which 
this took place, I filled the vertical parts of the U-tube up to 
as many different heights as possible with the liquid, and re- 
peated the experiment. Again b and c remained indifferent 
to one another; suddenly there was a violent deflection of 
the galvanometer-mirror; but at this moment the liquid on 
both sides began to place itself in equilibrium. According 
to these experiments, chlorine does not penetrate palladium as 
hydrogen does. 

From this I think Iam warranted in maintaining, generally, 
that, strictly speaking, we never have to do with any electro- 
motive force of gases, but either with tension-differences 
called forth by conducting liquids of different kinds, or with 
alterations of metals by gases which have lost their gaseous 
state by occlusion in, or condensation on the surface of, 
metals; for an actually coherent layer of gas that covered a 


14. On Electricity at the Contact of Solids and Cases. 


metallic conductor would surely insulate it from the conduct-. 


ing liquid. 

I will here add the description of an experiment which I 
made, long ago, for the purpose of getting an explanation of 
the activity of gases in the gas. battery. Gaugain, in the 
paper above mentioned, has advocated the view that the elec- 
tromotive force of the gas battery is to be attributed solely to 
the chemical ‘affinity with which the oxygen of the water and 
the hydrogen condensed by the platinum act on one another. 
To this I objected that this proposition must be generalized, 
since other gases also act as electromotors ; it must therefore 
be expressed something like this:—A gas acts as an electro- 
motor through combining, under a catalytic cooperation of 
the platinum, with one of the elements of the water™. 
Whether this proposition is correct can be ascertained by the 
following experiment. In a dark room I filled up two tubes, 
in each of which was a platinum plate, and containing, as 
usual, diluted sulphuric acid, with chlorine. The two plates 
showed no difference of tension. I now covered over one of 
the tubes with a yellow-glass bell, and let the daylight fall 
upon both tubes. Certainly the action of the chlorine upon 
the hydrogen of the water was now much more vigorous in 
the free than in the covered tube; but no difference of ten- 
sion was visible. For chlorine, therefore, the above proposi- 
tion is certainly untenable. To hydrogen it is indeed still 
less applicable, since otherwise the affinity of the hydrogen on 
the platinum for the oxygen of the water would have to be 
greater than that of the oxygen for the hydrogen already com- 
bined with it. 

I remark finally, in reference to Graham’s statement 
(already called in question by G. Wiedemann?) that palla- 
dium charged with hydrogen is strongly magnetic, that I 
have never succeeded in detecting any action of hydride of 
palladium upon the magnetometer. : 


After the above communication had been presented to the 
Royal Academy, I received the April number of the ‘ Philo- 
sophical Magazine,’ in which Mr. Morley publishes an inves- 
tigation, carried out by him in Professor Foster’s laboratory, 
on Grove’s gas battery. Mr. Morley is only acquainted with 
the older writings of Grove and Schénbein and the newer 
ones of Gaugain; mine he seems never to have seen. 


* Pogg. Ann. cxxxil. p. 458. 


t Galvanismus, 2nd. ed., vol. i. p.528; cf. Blondlot, Berd/. vol. i. p. 634. _ 


On the Mechanical Theory of Crookes’s Force. 15 


- He, likewise, controverts the view that the seat of the elec- 
tromotive force in gas batteries is the place of contact of 
metal, liquid, and gas; but he comes to the conclusion which 
in the present communication I have declared is not univer- 
sally valid—that the entire current of the gas battery owes its 


- rise to the dissolved gases. At the same time he does not 


admit that the gradual falling-off of the current of a closed 
gas battery is to be attributed to polarization coming in, but 
seeks its cause solely in the diminution of the volume of gas 
dissolved in the liquid. As, however, he does not measure 
the electromotive forces by momentary closings of the circuit, 
as Gaugain and I have done, but calculates them from the 
eurrent-intensity observed during a continued closing, and 


from the resistance, it is not possible from his measurements 


to distinguish the primary from the secondary actions. That 
a mixture of this sort has not been avoided is shown also by 
the proposition at which Mr. Morley arrives :—that the elec- 
tromotive force of the gas battery is not constant, but increases 
with the resistance. 


Munich, May 1878. 


Il. On the Mechanical Theory of Crookes’s Force. 
By GEorcE Franois Firzcerayp, I.A., F.T.C.D.* 


HEN two surfaces at different temperatures are in pre- 
sence of one another with a gas between them, there 
exists a force tending to separate them. The assumption of 


_ this force explains a very great number of phenomena, inclu- 


ding the motion of the arms in Mr. Crookes’s radiometers, 
and the so-called spheroidal state of liquids. That this force 
was due to some sort of unequal stress in the gas between the 
two surfaces, was pointed out by Mr. Stoney in the Philoso- 
phical Magazine, March and April 1876, where he attempted 
to show that such a state of stress would arise. An attempt 
to explain the motion of the arms of a radiometer had been 
made previously by Professor O. Reynolds; but his conclu- 
sion, that it was principally due to evaporation and condensa- 
tion, is manifestly inadequate to explain a continuous action, 
such as that in a radiometer; and the method by which he 
tried to show that a surface, when communicating heat to gas, 
is subject to an increased pressure, is open to the overwhelming 
objection that this increased pressure would be almost instan- 
taneously transmitted to all parts of the enclosed gas, and so 


* From the Scientific Transactions of the Royal Dublin Society for 
October 1878. Communicated by the Author. 


16 Mr. G. F. Fitzgerald on the Mechanical 


could not possibly be the source of such a force as would ex- 
plain the motion of the arms of a radiometer. 

In amplification of a letter I wrote to ‘ Nature’ on the 17th 
of December 1877, and which was published on the 4th of 
January, 1878, I now intend to prove that such a state of 
stress as Mr. Stoney’s theory requires would exist under the 


assumed conditions. My letter contains a proposed applica-— 


tion of Clausius’ investigation for finding the conducting- 
power of a gas, as published in the Philosophical Magazine, 
vol. xxiil. 4th series. Mr. Stoney, in a paper read before the 
Royal Dublin Society on Monday, the 18th of February, 1878, 
[ Phil. Mag. Dec. 1878, p. 401] has obtained results some- 
what like those obtained by my method by applying a method 
similar to one he originally employed. 

I may first observe that the only way in which a state of 
other than uniform stress can exist in a gas is by the distribu- 
tion of the mean velocities, and number of molecules, being 
different in different directions, or, as Mr. Stoney has called 
it, by the gas being polarized. That the distribution is not 
uniform when heat is being conducted through a gas has been 
pointed out long ago by both Clausius and Maxwell ; and what 
is required is, to show that the distribution will then be such as 
to develop a force like Crookes’s. 

Following the method adopted by Clausius in his paper 
already referred to, I assume that the mean velocity of a mo- 
lecule is a function of its direction of motion, and that the 
number of molecules in the unit volume moving in a given 
direction is also a function of that direction. If, then, we 
define the direction by means of yp, the cosine of the angle it 
makes with a given direction, ¢ the angle the plane of these 
two directions makes with a fixed plane through the given di- 
rection, we may evidently assume 


v=v,f(uh), n=nF (ud), 


where v and n are the mean velocities and number of mole-- 


cules moving in this direction, and v, and n, are certain given 
values of v and nm when f and Fare unity. Now we may eyi- 


dently in addition take n= es N du d¢@, where N is the total 


number of molecules per unit of volume; so that we have, 


generally, < 
ray F(u, $)dp do. 


The quantities I intend to calculate are—the number of mo- 
lecules carried through the unit area in any direction, the total 


ee a 


Theory of Crookes’s Force. 14 


momentum carried through the same, and the quantity of 
energy carried through it. The number of molecules going 
in one direction through the unit area must evidently be equal 
to that of those going in the opposite direction, if there are 
no gaseous currents going on; and even if present, their ex- 
istence is evidently beside the question in hand. Hence, if 
we sum the number of molecules passing the unit area, taking 
those that go in opposite direction through it with opposite 
signs, the sum must vanish. I shall calculate the numbers in 
three cases of unit areas :—I1st, perpendicular to the line from 
which 7 is measured, or X; 2nd, parallel to the plane from 
which ¢ is measured (i. e. perpendicular to Y); and, 3rd, for 
the case of a unit area perpendicular to these two (i. e. per- 
pendicular to Z). The number of molecules going in the direc- 
tion (“, d) that pass through the first of these per unit of 
time is evidently =nvy; and it is likewise evident that the 
number going in the opposite direction will have an opposite 
sign ; so that we have the sum of all such zero. Similarly, for 
the other two planes the numbers are 


nvr/ 1—p?. sin o@ and nvr/ 1— 2". cos db; 
so that we get 
O=Lnvp=Zaw/1—p? sin = Tnvr/1—p*. cos ¢. 

The momentum carried through the first of these unit areas 
per unit of time by molecules moving in the direction (, ¢) is 
= Mnv7p’, if M be the mass of each molecule ; and as it does not 
change sign with #, we see that the sum of all such will repre- 
sent the normal pressure per unit area at the given place. We 


can similarly get the normal pressures on the other two unit 
areas; and calling them P,,, P,,, and P,., we obtain 


Pa Sa 2”, 
Py, = M2nv?(1—p?) sin? ¢, 
P.,= M2nv?(1—p’) cos? 4. 
Proceeding similarly, we can get the tangential pressures 
on these areas; and we easily see that they are 


Pyz= P= M2nv?(1—p”) sin ¢ cos 6, 
Pir= Pyz=M Env pw/ 1 — pL. cos d, 
1 pe MS nv?p/1—p2. sin op. 

If now we proceed to calculate the energy carried across 
these areas per unit of time, we get knv*u as that carried across 
the first area by molecules moving in the direction (wu, 6) when 
k is the coefficient by which the energy of translation must 


Phil. Mag. 8. 5. Vol. 7. No. 40. Jan. 1879. C 


18 Mr. G. F. Fitzgerald on the Mechanical 


be multiplied in order to obtain the total energy. Calling the 
quantities of energy Q,, Q,, Q., we thus get 


Q,= Mkinvi xp, 
Q, = MkEnv*/1—p? sin ¢, 
Q.= MkEnv/1 —p? cos . 
In order to be able to perform these summations, it is ne- 
cessary to know the mean values of nv, nv”, and nv? in terms 


of » and ¢; and I shall, in the first place, merely assume that 
they can be expanded in a series of spherical harmonies, thus: 


Wad er 
nv = qo(AotArtAet. . .)du dd, 


abe Nab 
Fie ie (B,+B,+ Bo+...)dud¢, 


ia (0, eee 
Mo = ek ot fa gt...)dudd. 


The effect of this is to obtain our former results under the fol- 
lowing simplified forms. Our first series of equations gives 
A,=0; and as A; must be of the form 


Ay=ayp + ayr/ 1 — sin d + a/ 1p COS d, 
we get 


== 6, 0,2—0: 


The second system of equations gives 
MNv? 
Pro= G— JJ (By + Bo)u'dy dé, 
MN? : 
Pyy= "(By + Bs)(1—n2) sin? $ du de, 


MNv’? 
P= oa \\(B + Bz)(1—p*) cos’ 6 du dd, 
MNv? 


Py= Py= §\B.(1—p7) sin $ cos $ du dé, 
MNv? ibs hs 
Pro Pas Go °() Byur/1—p? cos $ dud, 


MNv®2 SRS 
Pay=Pyo= Gf) By 1p? sin dude. 


ee ey eS ee ee ee 


—— ee Oe 


eemetnneieiteiietinatienen Te alee ee ee 


lit he 9 - 


There of Crookes’s Foree. 19 
If now we assume 
B,=b,(u?—4) + b(1—p”) cos 26 + b3(1—y”) sin ¢ cos p 
+ bywr/1—p? cos db +b;u\/ 1 —p? sin 4, 


as it must be of this form, we get, on putting our other quan- 
tities into the forms of spherical harmonics, 


— MNe? + 
P= — 3! (B+ 75 -h1); 


ie 2 2 
P= 3 MNe:(B, — b;— 5 bs), 


pil 5 MNo?(B,— + Bp = ba), 


3 15 E 
Ps MNvt,=P 
y= 15 INV) Sore 2p 
ik 
Pes = 75 Ne iN Ba 
1 
Pag iB MNv2b;= Pye 


Similarly, for the quantities of energy transferred we get 


G- a *i Sf Cuid ud, 


Nv 
Q,= = NOVI —p’ sin d du dd, 


ue 
Q.= kif OVI=p? cos $ du dg ; 


so that if we assume, as we evidently may, 


C,=cywetoVv1—p’ sin ¢d+e;V 1—p? cos , 
we get 


@- : MNv%y,, 
k 3 

Q,= 3 MNvieo, 
epee? 

= 3 MN U3C3e 


Hven in this most general form we can see that there will 
in general be a difference of pressure in different directions; 
C2 


= ——————— 


20 Mr. G. F. F itzgerald on the Mechanical 


for it is evident that the pressures in the three directions can- 
not be equal unless 6; and b, both vanish, which will not in 
general be the case. Without a knowledge of the nature of 
the distribution of the velocities and numbers of molecules 
moving in the different directions, it would be impossible 
to calculate the values of 04, ba, 63, b4, and 6;; but I think 
we can see that they will in part at least vary as the square 
of the quantity of heat passing. This can be seen from 
the following considerations. No matter what the distri- 
bution of the velocities and numbers of molecules moving in 
the different directions may be, it is plain that terms occur- 
ring in the coefficients of V1—p’ sin. ¢V 1—wp’ cos¢ (i. e. 
in the spherical harmonics of the first order in wu and v) will 
occur in the terms of the same order in nv nv” and nv*, and 
that linearly; while these same terms will occur squared 
in the spherical harmonics of the second order in nv nv’ and 
nv’, Hence we see that terms occurring linearly in the sphe- 
rical harmonics of the first order in nv’ will occur as squares 
in the spherical harmonics of the second order in nv?; so that 
b,, by will contain ¢;, cz, and cz in the second degree, 2. e. will 
contain terms varying as the squares of the quantities of heat 
passing. It is also to be observed that terms occurring in the 
spherical harmonics of the second order can never come into 
those of the first, except as products with terms belonging to 
spherical harmonics of the third order; so that a hypothetical 
distribution which gave correct values for the quantities of 
heat passing might very well be quite inadequate as a means 
of calculating the difference of pressure in different directions. 
This remark is of importance when we come to consider the 
results of Clausius’ hypothesis, and was suggested to me by 
Mr. Stoney in conversation. 

As an example of what I am insisting upon, we may take 
two opposite extreme cases :—first, the case of B, vanishing, 
and, secondly, the case of C,; doing so. In the first case there 
would be a distribution of velocities and numbers such that, 
though heat would be conducted across the layer, nevertheless 
there would be no resultant inequality of stress; while in the 
second case, though no heat would be conducted, yet there 
would be inequality of stresses. It seems, however, certain 
that neither of these extreme cases can exist as a permanent 
distribution in gases. Before calculating the values of these 
quantities upon particular hypothetical distributions, it may 
be well to see what they are in the simple case of two parallel 
planes, each at a uniform temperature. 

In this case it is evident from symmetry that, if we take X 
normal to the planes, we must have all our equations indepen- 


4 — ee ee ee a a 


— 


so that, calling 


‘Theory of Crookes’s Force. 21 


dent of ¢, as the effect is evidently symmetrical with regard 
_to X. Then we get 


bp = b3=b,=b;=0= 02 =Cs, 
and there are no tangential forces, while all the heat is trans- 
ferred in the direction and our eon become 


po 5 Me 2(B, mae sh), 


Pyy=Pee= 5 MN0 , -54), 


, while the heat transferred is 


Q.= 5 MNvve, 


The excess of pressure in X over that in the normal directions 


is 


Poe—Py= 7 MND, =K 5 


- and this has been called Crookes’s force. 


That it depends wholly upon 0, can be seen by the following 
simple method, mentioned to me by Mr. Stoney. 
Our expressions for P,, and P,, are 


P= MS np", 
P,y= MEnv?(1—p’) sin’ d ; 


N 
arr Ps Idy dd, 


when I depends upon the distribution of numbers only, we can 


write the pressures 


jee =o bet wae dd, 


MN 
Pane TEs iP cue! —p?) sin’ddpu dd. 


We can integrate them with respect to 6; for we know that 
Iv” is independent of ty in the case we are considering ; 


oy iP ee 5 MNJ Iv?u"*dp, 
a= _ Eaava) Iv?(1—p?)dp; 


+. Pag Py =e= G MNS Te°(u?—Y)dp 


22 Mr. G. F. Fitzgerald on the Mechanical 


so that if Iv’ be expanded in spherical harmonics, K depends 
only upon the spherical harmonic of the second order. Simi- 
larly, if Iv’ be similarly expanded, it is easy to see that 


— ly, 
Q,= 9 MN& { 8 udu 


an only depend upon the spherical harmonic of the first order 
“ay ne 

If now we turn to particular hypotheses as to the character 
of the distribution of velocities and numbers, the first that 
claims our attention is Clausius’s. He starts from the assump- 
tion that the distribution of velocities among the molecules 
that have just encountered one another in any given layer may 
be perfectly represented by supposing a small constant velo- 
city in the direction of the transference of heat to be super- 


posed upon a uniform distribution. This is the same as sup- — 


posing that these velocities in various directions may be repre- 


sented by the radii drawn to the surface of a sphere from a> 


point slightly displaced from its centre. It is worthy of 
remark, in connexion with what I mentioned before with refer- 
ence to the way the quantities in the various spherical har- 
monics are related to one another, that, supposing the sphere 
to be an ellipsoid of even greater ellipticity would not have 
affected his results; for it is easy to show that the ellipticity 
of an ellipsoid of revolution only enters into the spherical har- 
monics of the second and higher orders ; so that it would not 
enter into the equation giving the quantity of heat, except when 
multiplied by terms of at least the order of the quantity of heat. 
Thus, even though the square of the ellipticity were of the order 
of the displacement from the centre of the point from which 
the radii representing the velocities are drawn, nevertheless 
that would at most only have introduced terms depending 
upon the product of these two, which would not have mate- 
rially affected his results. Hence we see that Clausius’ suc- 
cess in calculating the quantity of heat conducted is no proof 
that his hypothesis is by any means a sufficient représentation 


of the actual distribation for the purpose of calculating the © 


resultant stresses; and that it is not is proved by calculating 
what the Crookes’s force would be upon his hypothesis. If this 
be done with the help of the quantities he gives in his note (see 
Phil. Mag. [IV.] vol. xxiii. p. 526), we get 

ze 1.8 plot Cy 


ke ear 


and the pressures deduced from this formula are very much 


smaller than those observed; so that it seems certain that the. 


> 0 — i a Cadi ett, ie Ae th 


Theory of Crookes’s Force. 23 


hypothetical distribution Clausius assumed is not at all ad- 
equate to represent the actual one. The pressures obtained by 
this formula are so insignificant that it is not worth while 
giving the details of the method by which it is deduced. That 
Clausius’ hypothesis is by no means adequate, can also be seen 
by the consideration that it is only after the Clausian laws for 
the conduction of heat have ceased to apply, owing to the 
rarefaction of the gas, that Crookes’s force becomes remark- 
able, as well as by considering what the distribution tends 
towards, as has been done by Mr. Stoney, in his paper pub- 
lished in the December Number of this Magazine. He shows 
that the distribution lies between one which could be repre- 
sented by two unopposing streams of molecules, moving one 
towards the heater and the other towards the cooler and un- 
polarized gas. With such a distribution the laws of conduc- 
- tion of heat would, of course, differ somewhat from those de- 
duced from Clausius’ distribution. 

I shall now calculate the result upon an arbitrarily assumed 
distribution, which, however, probably represents the actual 
one more nearly than Clausius’s. I shall assume that the dis- 
tribution of velocities can be represented by the formula 


v=v,(lt+acosd+P sin @singd+ysin @ cos¢ 
+acos6+bsin?@ sin’ ¢ + csin? @.cos’p+2f.sin? Asin dcosh 
+29 sin @.cos@.cos@+2hsin @. cos @.sin d, 

where 
cos 0=p. 


This is equivalent to saying that it is represented very nearly 
by the radii drawn to the surface of a slightly elliptical ellip- 
soid from a point near its centre. I shall assume that 2, B,y, 
a,b,c, f,g,h are all quantities whose squares and products may 
be neglected. For the number of molecules moving in the 
given direction 0, ¢, I shall assume that it varies inversely as 
the velocity of the molecules moving in that direction, so that 
nv=Nv,. This evidently satisfies the condition A,=0. By 
these assumptions we obtaiii approximately nv?=Nv,.v and 
nv’ = Nv, .v*, and hence 


([ltap+BV1—psindt+yV1—p. cos d 
2 Ne = = 7 1-— 2 : 2 

mea, +b(1—p"*) sin"d + (1 —p") oP ! 

| +2fV/1—p’ sin d cosf+2quVv 1—p’. cosh 

\ +2hw/1—p?.sin d], | 


24 Mr. G. F. Fitzgerald on the Mechanical 


or, turning it into the form of a series of spherical harmonics, 


( 3 Aa ) 
| 1+ 5(atb-+e)+ (a— sore) —b) 


1) Oe 
no? = Not + 5(c—5) A — ) cos 2p : 


+2f/1—p’. sin g cos 6 + 2guV 1—p’. cos p 
+ 2/uV1—p*.sin ? 
+anw+8BV1—p’.sind+tyvV 1—p’-cos ¢, 


from which we see that 
h=a—Z(bte), b= 5 (c—d), 
2 (pes 29, 40 


We may evidently include the 5 (a+ b+c) in the mean value 
of Nv?, and take B,=1; so that, calling MN=p the density 


of hp a our pressures become 
Peo= 5 0rs[1+ 5 (a—5 (+6) } 
rom bras f (0—Love)h 
va= v8 1 + Bb = (c= ; (a+0)) | 
w= Tp Po S = Pay, 
P= - pry 9 = Paz, 
Pay = “ PUse i — lay e 
Similarly, from nv? =Nv,.v? we can get 


C= 20, ic 2 owe, 
and hence 


— 9 
Q.= 5 = Tpes a, Q,= 5 - kere -B, Q,= 5 kpy,- ¥- 


Theory of Crookes’s Force. 25 


The normal pressures may also be put into the form 
1 1 1 
— 5 Pv: { 1+ 73 (a+tb+c)+ 5 (a—b—c) \ 
Pie {1+ Gene =(b—e-a) 
yy 3P 0° 15 5 ? 


Tey x 1 1 
Pez = 3 PU {1+ pp ttotot s(c—a—b) bs 


so that the state of stress is a uniform pressure, and super- 
posed upon it a system of pressures represented by the equa- 
tions 


1 i 
1 3 P% 3 (a—b—c), 


iL ik 
Py 3 PX "5 (b—c—a), 


1 1 

Pez= 5 pry-7 (e—a—b), 
1 2 

Pye 3 pry: 5/ = Pex 
Lagat 

Pe 3 Pv: 5 J =Pee) 
1 g 

Pry = 3 P% ; 5 = Dye 


Now it is remarkable that, if | 
aa’ + by? + cz + 2yz+ 2gzx + 2hay = (le +my+nz)’, 


we should have expressions for these additional unequal pres- 
sures the same as Professor Clerk Maxwell gives (see his 


‘Hlectricity and Magnetism,’ vol. i. p. 129, and vol. ii. p. 256) 


as expressing that state of stress in the ether which produces 
electrical phenomena. In order to make them identical, all 


_ that is necessary is to put 


‘= Sar 
X=l 15 pv, 


Sir 
Yam, /% pr%, 

Sar 
Zany [5 prt 


so that the resultant unequal pressures in the gas may be. 


26 Mr. G. F. Fitzgerald on the Mechanical 
: . 
represented by a pressure pas when W?=X?+Y?+Z? in 
the direction given by 
we: V1—p' sind: Vl—wcosd:: X: Y:Z::l: m:n, 
and an equal diminished pressure in every direction at right 


angles to this line. Double this pressure will be the Crookes’s 
force, which is consequently in this case 


il. 1 
K= 3 PYG +5 (P +m? +n’); 


and it is in the direction whose direction-cosines are propor- 
tional to 1: m:n; ‘so that, if we put 


l=yn, m=vV1—p' sing, n=vv/1—p’' cos 9, 
1 
R= [pM 


The direction-cosines of the line of transference of heat are 


evidently a: 8: y,and:so far there is no reason why these two 


lines should coincide, although of course in most cases they 
probably differ but little in direction. 

The only other distribution I shall consider is one suggested 
by Mr. Stoney’s investigation (Scientific Transactions of the 
Royal Dublin Society, p. 39) of the nature of the distribution 
of the velocities in the gas between two large parallel surfaces 
at uniform unequal temperatures. He has shown that it tends 
towards a distribution which would be represented by two 
streams of unpolarized gas moving in opposite directions across 
the layer. Now the actual distribution is never’exactly this, 
and possibly, as he has mentioned, departs in various degrees 
from it as you pass across the layer. If, however, we assume 
the distribution to be the same all the way across, and that 
consequently the mean temperature of each stream is that due 
to the surface it is leaving, we can calculate the resultant pres- 
sures. 

If v, and v, be the mean velocities of the molecules in each 
stream respectively relatively to the centres of mass of the 
molecules, and if u, and u, be the velocities of the streams 
(2. e. of these centres of mass), and p; and ps their densities, 
the pressure upon a fixed plane normal to the direction of the 
streams is : 


1 1 
P= 5 P1v7 + 3 Pos +p,ui + Pou 


dha inlt” there: _— 


ee 


Theory of Crookes’s Force. 27 
while the pressure sideways is 
1 aa 
P= 3 Piri t 3 pars 
so that the Crookes’s pressure in this case is 
K=P—p=pyu? + pa2. 


In order that there be no accumulation of gas at either sur- 
face, we must evidently have 


Pity = Pog. 


If V2 and V2 be the total mean squares of the velocities of 
agitation, V?=v?+%w, Vi3=v2+u2, and the quantity of heat 


transferred is . 
= k(p,V uty —p2Vzu"), 
k being, as before, the coefficient by which the vis viva of 
translation has to be multiplied in order to get the total energy 
of the gas. 
From these we easily obtain 
Kp tr), 
Q=kpyu(Vi- V2) s 
 Q= PAG Vi- Vo. 
Uy + Ug 
We have besides p,+p2=p, where p is the density of the 
gas. Hence there are six equations between the six unknowns, 


P15 P29 V1y Vay U1y U2 


‘and in order to eliminate them and obtain an equation between 


K and Q, it is necessary to make one further assumption. I 
assume, then, that w,=Av, and w2=Avr, so that V?=(A?+1)u? 
and V2=(A?+1)u2. I assume this because, if le streams 
did ae interfere with one another at all, we should have 


a 
=e Via3 


so that, if 7+ 1=2?, we should have 


a’ =6 and a=2°'5 g. p. 
Our equations then become 
V,— V2=27(u?—w?) ; 
*, Q=kKe?(uy—uz). 
From these we can eliminate 1, ws, p1, p23 and putting 


Vi-Va=xX, 


28 On the Mechanical Theory of Crookes’s Force. 
we get 
Q)* ae ya ~ KQ"— ahi X* . K=0) 
which is a quadratic he Q’ or a biquadratic te K, 
Solving for Q, we get 


RK AV @ 
ee ian 


as evidently the other solutions are inadmissible. 

From this we may get an approximate value for K in terms of 
Q; for, unless « be very large, or the density or difference of 
temper ature very small, X’p is much greater than 2eK, For 
instance, if V, and V, correspond to a difference of 10° C., 


eo Mtely Xs 442K? —2K}*, 


Vi=4 shi 
V,=48500 T 
273 
and consequently 
en (48500)? , 
a SREY 
= X= 9 G00; 
while p=<J, for air at atmospheric pressure ; 
ep — 07 G00. 


And K would be large if it were 100; so that even if a were 
50, 2aK would still be less than 34, of X’p; and so we may 
take approximately 


a2 ee 
ka. X& 
From this we can calculate K; for =1-6 in most gases, and, 
if a=2°5, VYa=1'5, and X=9700, as above ; 
*. kex/ aX = 22310 =2 x 104 g. p. 


Now, at a distance of a fourth-metre in air at atmospheric 
pressure, and with a difference of temperature of 10° C., 


O= 10a war 
K 50% p.,! 


so that in this case 


soiadil 


re see - 


Mr. W. H. Preece on the Electric Light. - 29; 


which is within the limits of the quantities obtained in the’ 
case of the spheroidal drops on liquids. 

That by this formula K varies nearly as Q, and not as Q?, 

is not to be wondered at, because in the first place the for- 
mula only professes to represent an approximation to the true 
state of affairs, and in the second place it is only at distances 
and pressures at which the ordinary laws of conduction of heat 
cease to apply that it professes even approximately to repre- 
sent it. 
- The whole of these investigations are unsatisfactory to this 
extent—that I have been unable, from a consideration of the 
molecular encounters themselves, to discover what is the actual 
distribution of velocities even in the simple case of two parallel 
surfaces. This is hardly to be wondered at; for the problem 
is extremely complicated, and evidently depends upon the 
undecided point in molecular physics, namely the proportion: 
of the molecules encountering in a given direction that are 
thrown off in the various other directions. We might very 
well assume, with Maxwell, that they are uniformly distributed 
in every direction after the encounter ; but even this does not 
simplify the question sufficiently to bring it within my present 
powers of solution. 


Ill. The Electric Light. By W. H. Presce, Memb. Inst. 
C.E., V.P. Soc. T.L., Electrician General Post-Office, §c.* 


EF. | eee theory of the electric light cannot be brought abso- 

: lutely within the domain of quantitative mathematics, 
for the reason that we do not yet know the exact relation that 
exists between the production of heat and the emission of light 
with a given current ; but we know sufiicient to predicate that 
what is true for the production of heat is equally true for the 
production of light beyond certain limits. 

The work done in a battery, or any source of current-elec- 
tricity, is expended outside the battery in a closed circuit in 
the form of heat. When this heat acquires a certain tempe- 
rature per unit mass, we have light. If the heat be confined 
to a mass of metal wire like platinum, we have light by in- 
candescence ; if it be expended in the transference of minute 
particles of incandescent matter like carbon across.an air-space, 
we have the electric arc. ‘The exact relations between current, 
heat, temperature, mass, and light have yet to be determined 
by experiment. 

.2. The are is thus a form of energy developed in one point 
* Communicated by the Author. 


30 Mr. W. H. Preece on the Electric Light. — 


of a circuit, which is the exact equivalent of another form of 
energy expended in another point of the circuit. Thus, if we 
produce light by a galvanic battery, it is the equivalent of 


chemical work done in the battery. If it be produced by a 


dynamo-machine driven by a steam-engine, it is the equiva- 
lent of coal consumed in the furnace. ‘The object to be at- 
tained in any economical utilization of this energy is to con- 
vert the greatest possible portion of it into light. 

3. Now the relations that exist between the work done, the 
current flowing, the resistances present, and the heat deve- 
loped are easily demonstrated. The work done (W) in any 
circuit varies directly with the electromotive force (#1) in that 
circuit, and with the quantity of electricity (Q) that passes 


through it, or 
W=EQ; 


but by Ohm’s law the electromotive force is equal to the pro- 
duct of the resistance (R) of the circuit, into the current (C) 
flowing, or ; 


E=CR; 


and by Faraday’s law the quantity of electricity passing de- 


pends upon the strength of current (C) and the time it flows 
(t), or ; | 


Q= Ct. 
Therefore, substituting these two. values in the above equation, 
we get 
W=C’Ri; 


in which we have what is known as Joule’s law, which gives 
us the work done (W), or its. equivalent, the heat generated 
(HH) in any circuit. By regarding the time as constant, we 
can put the equation _ 

: B=OR sao) 


4, Now let us take the case of a battery whose electromo- 
tive force is H and whose internal resistance is p. Let the 
resistance of the connecting wires be vr. Let us also have a 
particular resistance /, which may be a wire to be heated to 
incandescence, or a lmpp to be lit by the arc ; then by Joule’s 


law (1), H=Cp+r+/); 
oe oe 
7 ye 

HB 
~ptr+l 


but by Ohm’s law, 
C 


— ‘ 


ee er ee ee ee ee aa 


Mr. W. H. Preece on the Electric Light. 31 


5. Confining our attention for the present to the heat gene- 
rated (H), this will be distributed throughout the circuit ; and 
that in the resistance (7) will be 

gt chalet S (2) 
ptr+tl (ptrt+)™ " * °° 
Now if we suppose 7 resistances in circuit joined up in series, 
then the total heat generated will be 
EPnl 3 
H/= ~———_x5. . - we 
If we differentiate this fraction with respect to ni and put it 
equal to nothing, we can find when the heat generated in 
these resistances becomes a maximum ; that is, 

Placa Sal 

dnl (p+r+nl)* 
whence 


[(p+r+nl)?H?—2HP?nl(p+r+nl)|=0, 


‘ ptrt+nl=2nl ; 
that is, 
ptr=nl; 


or the greatest heat is generated in the resistances when the value 
of the latter equals the resistances of the rest of the circuit. 
6. Let us now assume the n resistances to be connected up 


in multiple arc; then the joint resistance will become . and 


the heat generated will be 
BE 


Ht : oo ae et en eh ie (4) 


and the maximum amount of heat will occur, as before, when 
U 
ae 


7. Now, in the first case, if the internal resistance of the 
battery and of the connecting wires be very small compared 
with nl, we may neglect them; so that by putting p+r=0, 
equation (3) becomes 

Hee 


ae 
or the total amount of heat generated in the resistances will vary 


inversely us the number of the latter in circutt. 
8. In the second case, we cannot neglect p + 7; for here the 


32 Mr. W. H. Preece on the Electric Light. 


greater we make n, the smaller “ becomes with respect to p+73- 


so that if eventually : becomes very small, we may neglect it — 


in the denominator of the fraction. Then 


1 
. 
a i B27 


“Gi ape @ 


so that in this case also the total heat generated in the resistances 
will vary inversely as the number of the latter in circuit. 

9. Now it must be observed that in each of these cases the 
total heat is distributed over n resistances; and therefore, as 
compared with one resistance, the heat generated in each is 


only ! 2 of that generated in one. So that, joined up either in 


series or in multiple arc, the heat generated in each of a number 
of resistances varies inversely as the square of their number. 

10. With respect to the ight emitted, if the amount of heat 
generated represented exactly the amount of light emitted, 
then the above equations would indicate the effects produced 
by multiplying the lights or subdividing the current when a 
constant battery is employed. But this is not so. The light 
obtained is not proportional to the heat generated. Below a 
certain limit the production of heat is not accompanied b 
light at all. In the case of incandescence, if the heat be dis- 
tributed over two wires instead of one, inasmuch as the mass 
to be heated in the one case is double that in the other, the 
actual temperature to which each of the wires will be heated 
will be only one quarter of that obtained with one wire, and 
the total light emitted will be half what it was before. In 
the case of the arc a similar result probably takes place: the 
incandescent matter, which is heated by the current and which 
gives out the light, is increased by the addition of each lamp, 
and therefore diminishes the actual temperature of each are, 
and consequently diminishes the light given out in direct pro- 
portion to the number of lights. 

11. Moreover, in the are the actual disintegration of the 
carbons and the transference of matter across the air-space, 
represent an amount of work done which must be deducted 
from that converted into heat, and which again tends to dimi- 
nish the amount of light emitted. If, therefore, the lamps be 
joined up in series or in multiple are, the light emitted by each 
lamp will vary inversely in a greater ratio than the square of 
the number in circuit. 

12. We have assumed E to be constant; but if the current 


} 
} 
f 
j 
7 
: 
° 
| 
P| 
4 
: 


Mr. W. H. Preece on the Electric Light. 33 


be produced by a magneto- or dynamo-machine worked by a 
steam-engine consuming a given amount of coal per unit time, 
E is no longer constant, for it varies with the resistances in 
the circuit. The constant in this case is the work done in the 
steam-engine in unit time. Calling this W,, the total heat 
generated in the circuit when the lamps are joined up in series 


]? e r . 9 e 3 = 


and since the light varies inversely as n (§ 10), the light 
emitted 


Ve ay ii euaee) 
and when joined up in multiple are, 
l 

ay Sor a) 


| ye ae 
cam) 
Or by putting p+r=0 in equation (7), and -=0 in the de- 


nominator of equation (8), we get 


and | 
Mike 
(ptr) 
So that beyond certain limits, when the current is produced 
by a dynamo-machine, if x lamps be joined up in series, the 


total light becomes diminished by i and the light emitted by 


L 


each lamp becomes diminished by i, 
n 
If they are joined up in multiple arc, the total light is dimi- 
nished by —, and the light emitted by each lamp = In the 


n”’ 


latter case the rapid diminution in the light emitted is due to 


the fact that the heat is developed in the machine itself instead 
of in the resistances external to it. 
13. We have assumed W, to be constant ; but this is only 


the case when a certain limit is reached, and when the velocity 


of the rotating coils in the dynamo-machine has attained a 


Phil. Mag. 8. 5. Vol. 7. No. 40. Jan. 1879. D 


34 Prof. H. F. Weber on the Inductions © 


maximum. This limit will vary with each dynamo-machine and 
each kind of lamp used. With the Wallace-Farmer machine the 
limit appears to be reached when six lamps are connected up 
in series. With the Gramme alternating machine and Jabloch- 
koff candles the limit appears to be five lamps. Beyond 
these limits the above laws will be true. It is this partial suc- 
cess in multiplying the light that has led so many sanguine 
experimenters to anticipate the ultimate possibility of its ex- 
tensive subdivision—a possibility which this demonstration 
shows to be hopeless, and which experiment has proved to be 
fallacious*. 


IV. On the Inductions that occur in the Telephone. By Pro- 
fessor H. F. Wresert. (Communicated to the Ziiricher 
naturforschenden Gesellschaft, at the Meeting of July 1, 
1878t.) 


\ | DUBOIS-REYMOND has given, is his “ Contribution 


to the Knowledge of the Telephone’’§, the following 

theory of the inductions that take place in the telephone:— 
The periodical variations of the electromagnetic potential P 
of the magnetic masses in the telephone in relation to the path 
of the current may, in the first approximation, be supposed 


proportional to the outbendings of the iron membrane. If _ 


the exciting membrane executes vibrations of the form 
>A sin (2anmt), then the periodical variations of the electro- 
magnetic potential are given by the expression 


P—P,=2B,, sin (2anmt), 


where P, denotes the value of P corresponding to the position 
of equilibrium of the membrane. M. Dubois-Reymond neg- 
lects the induction of the current-path upon itself as unessen- 
tial, and sets forth as the really active electromotive force only 


* Vide Fontaine’s ‘Electric Lighting,’ chapter xi. 

+ Translated from a separate impression, communicated by the Author, 
from the Vierteljahrsschrift der Zuricher naturforschenden Gesellschaft. 

+ Ten days later, on the lith July, 1878, M. Helmholtz transmitted to 
the Berlin Akademie der Wissenschaften a memoir in which he handled 
the same subject in the same manner. That already on the Ist July [had 
made known the contents of the present memoir is evidenced, enter alia, 
by the following, added by M. Hermann to his last paper in the Annalen 
der Physik und Chemie, new series, vol. vy. p. 91, on the 2nd of July :— 
‘Professor Fr. Weber, of Zurich, has succeeded in showing that the rela- 
tion found by me is in harmony with the law of induction, and that the 
latter has been wrongly applied in the theory which I have controverted. 
He will shortly make a communication on this matter.” 

§ Archiv fur Physiologie, 1877, pp. 573, 582. 


| 
| 


ee ee ee ee re 


that occur in the Telephone. ee 


that which results from the value of P according to the general 
law of induction: 
oP 


K= ae =2B,,.2anm . cos (2arnmt). 


The current occasioned in the telephone is proportional to this 
quantity ; and so is the outbending of the excited membrane 


in the receiving telephone. If the air-vibrations which excite 


the telephone have the form 2A,,.sin (2rmt), the vibrations 
excited in the air by the telephone take the form 


LAn.2anm.cos (2anmt). 


Thus the tone (Klangfarbe) of the sonorous motion, is neces- 
sarily altered during its telephonic transit: the partial tones of 
a higher number of vibrations come out stronger than those of 
a smaller number. At the same time there is a phase-dis- 


placement to the amount of 5 ° 


M. Hermann has shown, in his ‘ Telephonic Notices ’’*, 
and in his last experiments, communicated to this Society, 
that these consequences of the theory of Dubois-Reymond are 


not verified by experience. Hermann instituted the follow- 


ing experiments :— 

I. In the circuit of a telephone one of a pair of coils was 
inserted, and in that of a second telephone the other coil, pa- 
rallel with the former. All the words and letters which were 
spoken into the first telephone could be heard distinctly out 
of the second. The same result still followed when a second, 
third, fourth pair of coils were in like manner inserted between 
the two telephones. From this M. Hermann infers that the 
induction is without any traceable influence upon the ratio of 
intensity of the partial tones of a sound; while, according to 
M. Dubois-Reymond’s theory, in these cases of multiplied 
induction a very considerable alteration in the tone must have 
occurred. 

II. Inan induction-coil oscillating currents, I, were excited 
by a vibrating magnetic tuning-fork placed near it. These 
currents were conducted to atelephone. In the circuit of the 
currents I one set of windings of a double-wound electro- 
magnet-coil of fine wire was inserted. The currents 1, induced 
in the second set of turns of the coil, were also, a commutator 
and key being inserted, conducted to the telephone. Moreover 
the telephone could at pleasure be taken out of the circuit of 


* Pliger’s Archiv fiir Physiologie, vol. xvi. pp. 264 & 314. 
D2 


36 | Prof. H. F. Weber on the Inductions 


the currents I or again inserted. One could thus investigate 
in succession the action of the currents I, the action of the 
currents J,, and the resultant action of the oppositely directed 
currents I and I,. It was found that the direction of the cur- 
rents I, was always the opposite of that of the currents I, that 
the currents I, exerted a somewhat feebler action in the tele- 
phone than the currents I, that the resultant action of the cur- 
rents when in the same direction amounted to nearly double 
the action of each singly, and that the resultant action of the 
oppositely directed currents was nearly equal to nil. M. Her- 
mann concludes from these experiments that the phases of the 


oscillating currents I and I, cannot be displaced = in relation 


to one another, that much rather they must nearly coincide. 

M. Hermann has, he believes, made it evident by these ex- 
periments that neither the amplitudes nor the phases of the 
partial tones of a sound are sensibly altered by the induction 
that passes in the telephone, and, accordingly, that the above- 
stated inferences from the theory of M. Dubois-Reymond do 
not correspond with the facts; whether, and how, the results 
of his experiments can be brought into accordance with the 
general law of induction he leaves undecided. 

The following communication is intended to show that the 
experimental results obtained by M. Hermann are in most per- 
fect accordance with the general law of induction, and can be 
adduced as new and interesting evidence for the universal 
validity of that law. This perfect accordance is attained as 
soon as all the inductions that take place in the telephonic 
circuit are taken into account. Dubois-Reymond has neg- 
lected the induction of the telephonic circuit in regard to itself 
as unessential ; it results from the following considerations 
that this induction is really the determining moment in the 
telephonic process. 

Let a telephone be in a closed circuit, and a second tele- 
phone be inserted in another closed circuit ; let both circuits 
be so constituted and placed that they exert upon each other a 
powerful reciprocal induction. 

(a) For that one of the two closed circuits which contains 
the exciting telephone T, let 

W signify the resistance of the circuit, 

I the current-intensity of this circuit, 

() the electrodynamic potential of this circuit upon itself, 

P the electromagnetic potential of the magnetic masses 
in the telephone T referred to the conduction of the 
current ; 


| 


that occur in the Telephone. 37 


(6) For the other closed circuit, which contains the excited 
Bi phone T, let 

W, sionify the resistance of the circuit, 

J, the intensity of the current excited, 

Q, the electrodynamic potential of this circuit upon itself. 
Lastly, let R be the reciprocal electrodynamic potential of the 
two circuits. 

The general law of induction furnishes, for the determina- 
tion of the two current-intensities : and I,, the two equations 


ye = ee 2 —R&, 
(1) 
fe = be oi Ro. 


Let the electromagnetic potential P have the form 


P=P,)+Asin (27nt). 
The equations 

I =C sin (27nt+a), 

I,=C,sin (27nt+a,), 
satisfy the equations (1), if the amplitudes C and S have the 
following values, 


eis A 1+(558) 


Q = A An ae a a 
IanQ * amid * ok QQ, —TanyGO 


(2) 


QQ / [sana t or ave au CmyGQ,| (3) 


and to the phases @ and a, the following values be given, 


W _2 W, 
pe ta [1+ (3) das cae wi sa 00 38 OB) 
L+ ee ) ee 
Wi 


27nQ, ery ab 
Pee pe es 
QQ, 27nQ/ \27nQ, 
If both telephones be in one and the same circuit, of which 
the resistance is W,, and the electrodynamic potential upon 


tan a;= 


(5) 


38 On the Inductions that ocour in the Telephone. 


itself is Q,, then we get from equation (2), as the expression 
of the amplitude of the resulting oscillating current, 


Ge is 


ee ed OO) 
Qo/ eo 


and the phase a, is in this case determined by the equation, 
resulting from (4), 


Sr Ngan 
tan a= QrnQ,’ Ran lee Sn tot rie © ite siiine kre Cae (7) 
The results obtained show :— 


(1) In the telephonic transit the tone is in general altered, 
since the amplitude of the oscillating current C, (and Gp re- 
spectively) is dependent on the number of vibrations n of the 
exciting potential P—that is, on the vibration-number of the 
exciting simple tone. 

(2) The phase-displacement that occurs during the tele- 
phonic transit is not a constant quantity; its amount changes 
with the constitution of the path of the. current, and depends 
on the number n of the vibrations. 

(3) In certain cases, however, the amplitude C, (and C, 
respectively) of the induced current becomes independent of 
the vibration-number n, and thus the tone of the exciting 
sound is unchanged. ‘This occurs as soon as the quantities 


eee tar alas 
27nQ ss 2arnQ, 
come out so small that their second dimensions can be neg- 


lected against 1. The resultant values for C, C,, and C, in 
this case are 


og tae gb PAL ay isi 
“=QQ—k AT QQaRP “= Q 
Under these circumstances the phases are determined by the 
equations 


Rianne 
ih eo 27 are) Qin 
7 OO 
fern (H2)a4 (Gr) 
ee QQi— 
and 
3 i 
tan = FenQo 


ee ee 


On Starch and Unannealed Glass under the Polariscope. 39 


The phase-displacements @, @, a, are accordingly small quan- 


tities of the same order, which in the limiting case 


Bees). Ws Py WY atic = =, 
Ian) Inn, oanQ, 

become =0. 
But the results deduced for this special case are the expres- 


sion of those obtained experimentally by M. Hermann. If it 


Ws d Wi 
27nQ ae 27nQ, 
were very small values in his experiments, then the complete 
agreement of the results of experiment with the general law 
of induction is demonstrated. By a closer consideration of 
the dimensions, the number of turns, and the resistances of the 
coils and telephones employed by him, we can perceive that 
the quotients mentioned actually were small values. 


can be shown that in fact the quantities 


V. Starch and Unannealed Glass under the Polariscope. 
By WaAuteER Batty*. 


[Plates I-IV. | 
y ce are many bodies, of which a spherical grain of 


starch and a circular plate of unannealed glass may be 
taken as specimens, having an optical structure symmetrical 
about an axis through the body. The object of this paper is 
to investigate the state of the light which emerges from such 
a body, when monochromatic light in any state of polarization 
is sent through the body in the direction of the axis. 
In fig. 1 (Plate I.) let SS’ and TT’ be drawn through R 
perpendicular to one another, and let U U’ and V V’ bisect 
the angles between them. Suppose a quarter-undulation plate 
to be fixed parallel to the paper, with its axes parallel to S 9’ 
and T'T’—and the light to be passed perpendicularly to the 
paper through a Nicol’s prism having its axis perpendicular 
to the paper and its plane of polarization inclined at an angle 
p to the line 8 8’, then through the quarter-undulation plate, 
and then through the body, which is also to be placed with its 
axis perpendicular to the paper. 

Let the paper represent a section of the light after it has 
emerged from the body. Take any point P and draw round 
it an ellipse representing the polarization of the light at P. 
The state of the light will be completely determined if we 
know the angle (#) which the axis major of this ellipse makes 
with RP, the angle (6) which a line joining the extremities 


* Read before the Physical Society, June 20, 1878. 


40 Mr. W. Baily on Starch and Unannealed 


of the axes of the ellipse makes with the axis major, and the 
direction in which the rotation takes place. 

Let the angle S RP=¢; produce RP to X and draw P Y 
1 PX; take any point Q on the ellipse, let P Q=7, and the 
angle QP X=. 

The resolved part of the vibration at P along RP has been 
retarded in passing through the body differently to the resolved 
part perpendicular to RP. Let the resolved part along RP 
have been retarded by a quantity o more than the mean amount, 
and the other part have been retarded by the same quantity 
less than the mean amount. The quantity o is a function of 
the distance RP. 

Let siné represent the vibration in the ether after the light 
has passed through the Nicol. This is equivalent to 

cos psinét | SS’ 
and 
sin psing — ie daly, 

After passing through the quarter-undulation plate the 

vibrations become 


cos p sin (¢ + 45°) | SS’ 
and 
sin p sin (¢—45°) | ee 
These may be written (the coefficient ne being omitted) 
cos p (sin t+ cos ¢) | SS’ 
and 
sin p (sin t— cos ¢) | 


It is easy to show that these vibrations represent motion in 
an ellipse whose axes are parallel to SS’ and TT’, and the ex- 
tremities of whose axes are joined by a line making an angle 
p with the axis major. 

These vibrations are equivalent to 


cos (ep — d) siné+ cos(p+¢) cost | PX 


sin (p—¢) sin ¢— sin (p+ ¢) cost | Pe 
After passing through the body the displacement || PX is 
x cos 8, and that || PY is7sin 6. Hence 


r cos 0= cos (p—¢) sin (t +o) + cos (p+ ¢) cos (+c), 
rsin@= sin (p—¢) sin (¢—o)—sin (9+ ¢) cos (t—c) ; 
which may be written 
| rcos@=a sint+b Cost, .° 4) 2) 
r sin 0=0a' sing +0’ Cost,«0) . kl Sen 


and 


en a ae ven > eh ee ie P< 


NE te nggierh LA er ee ee ea — 


Glass under the Poldriscope. Al 

where 
cos (ep—¢) cos g— cos (9 +) sing, 

b= cos(p—¢) sina+cos(p+¢) cosa, 

a= sin(p—¢)coso— sin(p+¢) sing, 

b‘= — sin (p—¢) sino— sin (p+ ¢) cosa. 
Differentiating (1) and (2) with respect to t, we have 
a0 _ 
dt 


8 
| 


cos 0S" — sin Br acost—bsint,. . . (3) 


a de BAG DB, st 
sin 07, + cos Or == a'cost iy Serer 3 


Multiplying (3) by 7 sin @, and (4) by 7 cos @, and subtracting, 
we have 
7” e =(asint+0cost)(a' cos t—86’sin t) 
—(a’sint + 0/cos t)(a cos t—b sin ¢) 
whence 


dé 

TS a pity Samy 

Lier Poke b—ab 
= sin 2p cos 2o0— cos 2psin2csin2¢. . (5) 
Again, in (1), (2), (8), (4), let ¢ have a value which makes 

: ‘e CE igh 
7a maximum or minimum; then @ becomes a, and ai vanishes. 
Hliminating v from (1) and (2), we get 
(asin «—a’cos a) sin¢= —(bsina—D’ cos a) cos ¢; 


and eliminating = from (3) and (4), we get 


(6 cose+0’ sin «) sint=(acosa+a’ sin a) cos t. 

Hence 

asina—a’cosa . bsina—b’ cosa _ 

bcosa+b/sine  acosa+a’sina ’ 
or 

2(aa’ + bb’) —(a? +B’ —a”?—b”) tan 2a=0; 

that is, 
sin 2p sin 2c + cos2p cos 2osin 2¢ + cos 2p cos 2p tan 2a=0. (6) 


Now 7” 2 is proportional to the area of the ellipse, as the 


period of vibration is constant; and the axes of the ellipse are 
proportional to sin 6 and cos 8, since the intensity of the light, 
and evnsequently the sum of the squares of the axes is con- 
stant over the whole section Hence the area of the ellipse is 
also proportional to sin 8. cos 6 (that is, to sin26). Putting 


42 Mr. W. Baily on Starch and Unannealed 


p=45° and c=0 in (5), we get peat, But in this case. 


the emerging light is circularly polarized, and consequently 
B=45°, whence sin 26 also equals unity. Hence in every 
case | 
SE mide a 
Hence | PeaeMaL ee ae . 
sin 2p cos 2o— cos 2p sin 2o sin 2@— sin 28=0. . (7) 

The locus of points at which the major axis of the ellipse of 
polarization is inclined at a constant angle to the radius RP 
will be called an “isoclinal line,’’ and will be denoted by the 
symbol K(«), where @ is this angle. K(a) and K(@—90°) 
are both included in the equation (6), as that equation does 
not distinguish between major and minor axes. ' 

The locus of points at which the line joining the extremities 
of the axes makes a constant angle with the major axis will be 
called an “ isomorphal line,’”’ and will be denoted by the sym- 
bol M(6), where 6 is thisangle. Hquation (7) is the equation 
to M(8). 

The direction of rotation of the ether is positive or negative 
according as sin 2/ is positive or negative—that is, according 
as ( is positive or negative, since we need only give 6 values 
lying between +45°. 

In figs. 2, 8, 4, 5 these loci are represented—the isomor- 
phals by continuous lines, and the isoclinals by dotted lines. 
The Arabic numerals indicate the values of # in degrees, and 
the Roman numerals those of 6 in degrees. 

The value given to ¢ is RP + 90°, a function which has been 
assumed solely for convenience in drawing the figures. The 
figures are drawn between the limits c=180° and c=360°. 
An extension beyond these limits would give merely a repeti- 
tion of the portion within them, since an addition of 180° to 
the value of ¢ makes no difference in the equations to the loci. 
Directions from the centres of these figures will be referred to 
by means of the lines in fig. 1. 

The values of p are in fig. 2, 45°, in fig. 3, 30°, in fig. 4, 
15°, and in fig. 5, zero. Accordingly the incident light is 
circularly polarized in fig. 2, elliptically in figs. 8 and 4 (the 
eccentricity of the ellipse being less in fig. 3 than in fig. 4), 
and plane-polarized in fig. 5. 

The isomorphals and isoclinals drawn are those for which 
the values of « and 6 are 45°, 30°, 15°, and zero. The thick 
continuous lines are branches of M(0), which is the locus of 
plane-polarized light. The round spots are loci of circularly 
polarized light, or M(+45). 


oe 


Glass under the Polariscope. 43 
~The symbol K( +a) will be used to include K(«), K(a—90°), 
K(—a), and K(90°—a); its equation is 
(sin 2p sin2o + cos 2p cos 20 sin 2h)? =cos’2p cos? 2¢ tan? 2. (8) 
And the symbol M(+ 8) will be used to include M(f) and 
M(—8); its equation is | 

(sin 2p cos 2o—cos 2p sin 2c sin 2$)?=sin? 26. . (9) 
Putting 90°—¢, or —90°—¢, for ¢@ in these equations 


makes no change in the equations. Hence K(+a) and 


M(+8) are each symmetrical with respect to UU’ and 
VV’. 
Adding (8) and (9), we get 
eos’ 26. cos” 2p = cos’ 2a. COs” 26, .. a = (10) 


from which equation it appears that the intersections of 


K(+e) with M(+8) all lie on the two diameters defined by 
the equation ; and since ae and 6 are interchangeable in the 
equation, we see that K(+y) and M(+6) intersect on the 

same two diameters at K(+6) and M(+y7). 


Let 
Sea Wy ate 
then K(+«) becomes 
(sin 2p cos 25— cos 2p sin 25 sin 26)?= cos? 2¢ cos? 2p tan” 2a, 
and M(+8) becomes 
(sin 2p sin 23 + cos 2p cos 25 sin 2¢)?= sin? 28, 


From these equations it appears that, in changing the sign 
of g, we shall change only the sign and not the magnitude of 
3S; so that if we have drawn part of K(+e) or M(+e) be- 
tween the limits 6=0 and @=45°, we can draw the corre- 
sponding part of the curve between the limits ¢=0 and 
g@=—45°. Ifo’ be the value of o corresponding to —¢, 


te 
f= (5+5)"-%, 


o+o'= (n+ 5). a ce we eT 


Putting 2=0 and 6=0 in (8) and (9), we get for K(0), 
| sin 2p sin 20+ cos 2p cos2osin2@=0; . . (12) 
and for M(0), ; 
sin 2p cos 2o— cos 2psin2osin26=0. . . (18) 
Let s be the value of o where a radius ¢ intersects a branch 


and therefore. 


44 Mr. W. Baily on Starch and Unannealed 
of M(0), and let s+ & be the value of o where the same radius 
intersects a branch of K(-+:«); then by (8) we have 
{(sin 2p sin 2s + cos 2p cos 2s sin 2p) cos 2& 
+ (sin 2p cos 2s— cos 2p sin 2s sin 2) sin 2€)}? 


= cos” 2p cos” 2 tan? 2a. 2... 2? Se 


But by (13) the coefficient of sin 2£=0, and & is determined 
by cos 2£ only, from which it appears that & has pairs of 
values of equal magnitude and opposite sign. Hence, if we 
have drawn a part of K(+ca) on one side of a branch of M(0), 
we can draw the corresponding part on the other side of M(0). 

A similar property of M(+8) with respect to K(0) may be 
proved in the same manner. 

Where K(+«) intersects M(0), & vanishes and the diameter 
becomes a tangent. Its position is determined by putting 
B=0in (10). This gives 

cos’ 2 cos* 2p— cos’ 2a. .  \).) es 
The position of the diameter tangents to M(+8) is determined 
by putting 2=0 in the same equation. We get 

cos’ 2 cos” 2p= cos" 28... 2 a la) 
Hence the same diameters are tangents to K(+y), M(+y) 
at the points where they intersect M(Q) and K(0) respectively. 

If we put o+45° for o in K(0) we obtain M(O), and con- 
peed: See equations (12) and (13). . . ara ke 

If we put «+ 90° for o in K(+<«) or M(+8), the equation 
is unaltered; and by this means from one branch of one of 
these curves we can obtain all other branches of the curve. (18) 

We will now consider the forms of the loci, dealing first 
with figs. 3 and 4, in which the incident light i is elliptically 
polarized. 

To obtain the isomorphals, we have the equation (7) for 
M(6) and (13) for M(0). 

Putting @=p, we obtain the following equation to M(p), viz. 


sin o(sin 2p sino + cos 2p cosa sin2¢)=0; . (19) 


and as B=—p, we obtain the following equation to 
M(—p), viz 
cos o (sin 2p cos o— cos 2p sino sin 2¢)=0.. . (20) 


M(p) therefore consists of circles for which sin o=0, and 
ovals intersecting those circles on the diameters SS’ and TT’; 
and M(—p) consists of circles for which cos7=0, and ovals 
intersecting those circles also on SS’ and TT’. The outer 
circles in the figures are circles of M(p); and the middle circle 
is one of the circles of M(—p). 


7 


Glass under the Polariscope. 45 


When 6= +45°, the light becomes circularly polarized, and 
therefore the value of « becomes indefinite; consequently in 
equation (6) we must have cos 2=0. Putting this value of 
cos 2h in (7), we get the following values of ¢, oc, and 6 at 
points where the polarization is circular:— 


p. o. B. 
+45°, n+ 45°+ ), —45° | 
+45°, nt+135°+p, § +45° 


rend 
—45°, n+ 45°—p, +45° ' oo 
—45°, nr+135°—p,  —45° J 


These points will be called the “circular points.” All the 
isoclinals pass through all the circular points. The sign of 6 
indicates the direction of rotation of the ether. Where the 
sign is positive, the direction of rotation has not been altered 
by the passage of the light through the body; where the sign 
is negative, the direction of rotation has been reversed. 

To draw the isomorphals :— 

Mark the circular points by (21). Draw the circles of 
M(p) and M(—p) by (19) and (20). Draw one branch of 
M(0) from ¢=0 to 6=45° by (13). 

Obtain a branch of K(0) by (17). 

Obtain an oval of M(p) between the above limits by (14). 

Draw the part of a branch of M(@), for example, M(XV.) 
in fig. 3, or M(X XX.) in fig. 4, which lies on one side of 
M(0), and complete on the other side by (14). 

Draw the remaining branches of M(+ 8) between the above 
limits by (18). 

Draw the isomorphals between 6=0 and d= — 45° by (11), 
and complete the figure by means of the symmetry about 
UU‘ and VV’. 

Write against the isomorphals the values of 6, taking care 
to make the sign of 6 the same as that at the nearest circular 

oint. 
; To draw the isoclinals :— 

Hquations (6) and (8) are not in a form available for cal- 
culation; but by solving (8) as a quadratic in sin 26, we 
obtain the equation to K(+a) in the form 


sin 2p cos 20 sin 20 cos” 2e + cos 2p(1— sin? 20 cos” 2a)sin 2h 
= ++ sin 2a (cos* 2p— sin? 2c cos’ 2a)2, . (22) 


from which, by putting successive values for o, we can obtain 
corresponding value of ¢. : 


By putting a=p, we obtain the equation to K(+p), viz. 
sin 2p cos 20 — cos 2p sin 20 sin 26=+sin2¢. . (23) _ 


46 Mr. W. Baily on Starch and Unannealed | 
We have already obtained a branch of K(0). Draw from 


(23) the part of a branch of K(p) which lies on one side of 


M(0) between the limits 6=0 and ¢=45°, and from (22) 
obtain a similar part of a branch of K(+:a«)—for example, 
K(15) in fig. 3 and K(80)‘in fig. 4. 

Complete these branches by (14). 


Complete the other branches between the same limits by 


(18). | 

Draw the figure between 6=0 and 6=—45° by (11), and 

complete the figure by the symmetry about U U’ and VV’. 
Draw straight lines in the direction U U’ and V V’ to give 

K(+45), for which the equation is 


sin2@=0. 0.) See 


To number the isoclinals :— 

Note in (6) that when o=n7, tan 2a= —tan 2¢, ora=—4; 
and when c=(n+34)z7, tan 2a=tan 2d, or a=+¢. Hence 
the intersections of the isoclinals with the circles of K(p) 
graduate that circle in the negative direction, and their in- 
tersections with the circle of K(—p) graduate that circle in 
the positive direction. Graduate these circles accordingly, 
taking care to deduct 180° from the graduation when it ex- 
ceeds 90°, and 360° from it when it exceeds 270°, and the 
readings will give the values of a. | 

The deductions are made to keep the readings low, and for 
the sake of symmetry. 

From the figures 3 and 4 it appears that M(+p) divides 
the figure into regions of two kinds: one kind, which I will 
call the ‘‘ segments,” contains all the points at which the light 
is more circularly polarized than the incident light; and the 
other kind, which I will call the “rings,” contains all the 
points at which the light is more plane-polarized. 

In the segments the isomorphals are closed curves surround- 
ing the circular points; and in the rings the isomorphals are 
closed curves surrounding the centre of the figure. 


It also appears that K(+p) divides the figure into regions - 


of two kinds—one containing all the points at which both 


the axes of the ellipse are inclined to the radius by a greater . 


angle than p, and the other containing all the points at which 
one of the axes is inclined at a less angle than p. Both 
kinds of regions are four-cornered, and have two opposite 
corners on circular points; but in the first kind both these 
circular points lie on the same radius, and in the second the 
circular points lie on different radii. The isoclinals in each 
region pass from one circular point to the other. 


nite 
‘ann 


es ee ee ee ee eee 


tak 


— Glass under the Polariscope. AT 


_ Comparing fig. 3 with fig. 4, we see that as p increases, 
the segments become smaller, and the isomorphals in the rings 
become more circular. When p=45°, as in fig. 2, the seg- 
ments vanish, and the isomorphals all become circular, the 
equation to M(6) becoming 


cos 2o— sin 28=0. 


The circular points are retained in the figure to show its 
relation to the other figures; but the whole circles through 
them are loci of circularly polarized light. 

The equation to K(+2) gives tan 2a=0 ; 


*, a= +45°. 
The equation to K(+p) becomes 
cos 2o= +sin 2¢. 


This curve is retained in the figure to show the continuity 
with the other figures—although, as the inclination is every- 
where 45° or —45°, the points on the curve have no special 
properties. or the same reason the straight lines K(+45) 
are retained. 

Again, comparing figs. 8 and 4, we see that asp diminishes, 
the segments increase ; and at last, in fig. 5, where p vanishes, 
the segments fill the whole space and the rings vanish. Hach 
closed curve of M(0) is forced into a broken line consisting of 
quadrants of circles joined by pieces of diameters ; and as these 
closed curves now touch at their angles, they form together a 
complete system of circles and diameters whose equation is, 
putting p=0 in (13), 


sin 2o sin 26=0. 


The isoclinal K(0) also forms a system of circles and dia- 
meters; their equation is, from (12), 


cos 20 sin 26=0. 


All the other isomorphals form closed curves round the cir- 


- cular points; their equation is, from (7), 


sin 2o sin 2¢+sin 28=0. 


And all the other isoclinals pass from one circular point to 
another on the same radius ; their equation is, from (6), 


cos 20 tan 26 + tan a=0. 
The diameters of K(0) and M(0) coincide ; this is indicated 


48 Mr. W. Baily on Starch and Unannealed 


in fig. 5 by the thick continuous line having dots on one side 
of it. 

The figure may be drawn in a similar manner to that de- 
scribed for figs. 3 and 4. 

The locus of plane-polarized light may be investigated 
without reference to the condition of the rest of the light, by 
drawing M(0) by equation (13), and marking the direction 
of polarization at successive points on it by equation (15). 

In figs. 6, 7, and 8 the points through which short straight 
lines are drawn are points at which the light is plane-polarized ; 
and the short straight lines through them show the direction 
of polarization at the points. The dotted lines connecting 
these points are loci of plane-polarized light. The centres - 
about which small circles are drawn are points at which the 
light is circularly polarized; and in fig. 6 the dotted lines 
connecting these circles are loci of circularly polarized light. 
The signs within the circles indicate the direction of rotation 
of the zther ; see (21). 

In fig. 6,p=45°; in fig. 7, p=—22" 30’; in fig. ogee: 

If the light be passed through an analyzing Nicol with its 
plane of polarization inclined at an angle p’ to SS’, we can 
obtain the intensity of the light at any point as follows :— 

The vibration along the major axis is cos B cost, and that 
along the minor axis is sinfsint; so that the vibration in 
the direction of the plane of polarization of the analyzer is 


cos (p’ —«) cos B cos t—sin (p’ —a@) sin 6 sin ¢. 


Hence, if I is the intensity of the light after passing the 
analyzer, 


I=cos? (p’—«) cos? + sin? (p’ —a) sin? B, 
21=1+cos2(p’—a) cos 26. 


The appearance of the light after passing an analyzer 
might be calculated from this equation, but can be inferred. 
more readily by an inspection of the figures, which show its 
state before passing. 

We notice that two dark spots will be seen on each branch 
of M(O), one at each extremity of a diameter, at the points 
where the vibration is perpendicular to the plane of the ana- 
lyzer. The spots on the successive branches of M(0) will be 
alternately on a certain diameter and on the diameter perpen- 
dicular to it. ) 

When the incident light is circularly polarized, these spots 
will move round in circles with unaltered appearance and at a 
uniform rate as the analyzer is turned uniformly. See figs. 


2 and 6. 


Glass under the Polariscope. Ag 


When the incident light is elliptically polarized, the spots 
will move round the curves M(0) ; but the rate and appearance 
will vary (see figs. 8, 4,and 7). For on the circles of M(p) 
the major axis ot the ellipse preserves a constant direction in 
space, since 6+a@=0; but on the circles of M(—p) the major 
axis rotates uniformly in space with an angular velocity double 
that of the radius, since 6—a=0. Hence in those portions 
of M(0) which are near the circles of M(p), the change in the 
direction of the vibration will be slow; so that in this part 
the spot will be elongated, and will move more rapidly than 
the analyzer is rotated: but in the parts of M(Q) near the 
circles of M(—p), the change in the direction of the vibra- 
tion will be rapid; so that in these parts the spot will be 
shortened, and will move more slowly than the analyzer is 
rotated. 

When the incident light is plane-polarized (see figs. 5 
and 8), the slow-changing parts of M(0) have combined to 
form the inner and outer circles of the figure and the diame- 
ters SS’ and TT’. Along these lines the direction of vibra- 
tion has no change, but remains constantly the same as 
that of the incident light; but on the middle circle of the 
figure, and on corresponding circles, the direction of vibration 
rotates uniformly with a velocity double that of the radius. 
Hence on the latter circles there will be spots moving uni- 
formly round with a velocity double that of the analyzer ; 
but on the other parts of the figure there will be no’ spots. 
However, when the spots on the latter circles reach the 
diameters, then the former circles and the diameters will 
become black. 

If the light is not monochromatic, these appearances will 
not be so distinctly seen, as the absence of one colour will not 
occur exactly in the same place as the absence of another, 
since the position of the isomorphal and isoclinal lines de- 
pends upon the value of oc, and this will differ for different 
colours. But the position of diameters which give plane- 
polarized light in figs. 5 and 8,.is not dependent on the value 
of o; and hence with any light this cross will always appear 
uncoloured, being black when the upper and lower Nicols are 
crossed, and in full light when they are parallel. 

If o is constant, the isomorphals and isoclinals become 
straight lines from the centre, and the state of the polariza- 
tion may be conveniently represented by taking a series of 
points in a circle round the centre, and drawing about each 
point the ellipse of polarization at that point. The ellipse 
will show the polarization along the radius on which it lies. 


Plal. Mag. 8.5. Vol. 7. No. A0. Jan. 1879. 10 


50 On Starch and Unannealed Glass under the Polariscope. 


This is done in figures 9 to 13, in which o is about 15°. In 
fig. 9, p=45°; in fig. 10, p lies between 45° and o; in fig. 11, 
p=s; in fig. 12,p lies between o and zero; and in fig. 13, p 
1S Zero. 

Suppose now the light to be passed through an analyzer 
placed with its plane of polarization in the direction TT’. 
When p=45°, the quadrants about U U’ will be dark, and 
those about VV’ will be light. They will gradually shade 
into one another, there being no black or full light. As p di- 
minishes, U U’ becomes darker until, when p=o, UU’ is 
black (see fig. 11). As p further diminishes, the black bar 
opens out into a dark oblique cross, neither bar of which is 
black ; and when p becomes zero, this cross becomes rectan- 
gular and black. As p passes on to —oa, the cross becomes 
oblique and not black, and closes up into a black bar along 
V V’; and when p becomes —45°, the quadrants about V V’ 
are dark, and those about U U’ light. When we have the 
oblique cross, we can by a suitable turn of the analyzer make 
either arm of the cross black. (Nee fig. 12.) 

If the analyzer is placed with its plane of polarization in the 
direction 8 8’, we get the same set of appearances, except that 
we get light for dark and dark for light; and in the case of 
the single bar and rectangular cross, we get full light instead 
of black. | 

The appearances presented when o is variable may be well 
seen in cylindrical disks of unannealed glass. I do not know 
of any bodies which show very clearly the appearances pre- 


sented when o is constant. Crystals of salicene show the © 


black cross remarkably well, and give indications of the single 
black bar; but in this substance o, though constant along 
each radius, varies in passing from one radius to another, and 
this completely hides the phenomena of the oblique cross. 
However, in grains of tows-les-mois starch, phenomena closely 
analogous to those above described as presented when a is 
constant may be easily observed under a moderately high 
power—the only difference in the phenomena being that, in 
consequence of the grain of starch being generally an un- 
symmetrical body, the lines are distorted, the black cross, 
for instance, being neither rectangular nor rectilinear. See 
“The Optical Properties of Starch,” Phil. Mag. for August 
1876. : 


. 


potty 


VI. A new Proposition in the Theory of Diffraction, and its 
Application. By J. Frouuicu, of Budapest. 


< eae mathematical expression which serves for the calcula- 

tion of the intensity of diffracted light leads, after a few 
simple reasonings, to a peculiar connexion between the kinetic 
energy of the diffracted light issuing from an element of a 
luminous surface and incident upon an infinitely large receiving 
screen, on the one hand, and, on the other, the energy of the 
light proceeding from a very large luminous surface and yet 
incident upon only one element of the screen. 

This relation is specially note-worthy on account of its faci- 
lity of application; for it gives a simple method of observa- 
tion which permits the question of the equality of the kinetic 
energy of the incident and the diffracted light to be at once 
decided experimentally for any aperture. : 

For the deduction of this proposition we make the following 
suppositions :— ; 

Let there be a diffracting aperture § (fig. 1), bounded by 
any p ane- or space-curve, Fig. 1. 
the dimensions of which 
relative to the wave-length 
of the light are very great, 
so that the amplitude of 
the diffracted light pos- 
sesses a finite value only ; 
when the angle of diffrac- 
tion is small, but other- 
wise vanishes. Further, let there be a uniformly luminous 
source of light of the form of a spherical surface F F, from 
which the light, after diffraction by §, arrives at the likewise 
spherical-surface-shaped receiving screen ff. The radii of the 
surfaces I’ F' and ff, p; and p,, are very long in proportion to 
the dimensions of the aperture; and their common centre O 
lies in the aperture or its immediate vicinity. 

Let the amplitude of the light-motion which emanates from 
the element OF be, at unit distance, ({¢dF)? (since each ele- 


ment OF vibrates quite independently of the rest); conse- 


quently there arrives at the diffracting aperture a motion the 


9? a 
amplitude of which is (20!)” which we shall in future de- 


Pi 
note by %;; hence it is the amplitude of the incident light 
proceeding from OF. 


* Translated from Wiedemann’s Annalen, 1878, No. 9, 


52 M. J. Frohlich on a new Proposition in the 
The motion of the diffracted light is of the form 


A sin (ans + 8) 


the general expression which contains its amplitude both for 
Fresnel’s and Fraunhofer’s phenomena is 


A=) Pike / GE Cos po 3) + (yee snpo F) } we 


in which 


Loom PE a 
Daa { 9 rue (2a+yB+ey) \; 


and x, y, z are the coordinates of the element 0% of the imagi- 
nary surface which covers the aperture and possesses its 
boundary, n the normal to this element; and 


a= cosa’—cosa,, B=cosBy—cosBy, y= cosy— cosy, 


if a; 8,91, 4) 8) % denote the direction-angles of the incident 
and the diffracted ray. 


The equation of the surface %§ can in any case be put 


z=¢(a, y), from which we get ge = cos (pn) as a function 


of andy; besides, 0F is = Seb the denominator of which 
can likewise be expressed by x and y; so that a function of « 
and y only stands under the integral-symbol of the above ex- 
pression, and the integration itself can be effected along « 
and y. 

The amplitude A is entirely independent of the position of 
the coordinate-system ; let us in future give it such a position 
that the incident ray, and therefore the a,@,y, direction, will 
fall very nearly in the plane of ZX; by this the following 
considerations will be simplified. | 

Upon the carrying-out of the integrations in A the variables 
a andy vanish; their place is taken by the constants of the 


limitation of the aperture ; and A depends on these and also — 


on p; and py, 4,8, y. Yet we have to do only with indefi- 


* The factor SP _ cos (p,”) follows from the principle of the equality 


of the kinetic energies, as will be shown in a subsequent paper. W. Voigt 
also deduced it from Fresnel’s theory (Wied. Ann. iv. p. 542 &e.), and 
likewise from the elasticity theory of light; it has, however, no influence 
at all upon the deduction or validity of the following proposition. 


Theory of Diffraction, and its Application. 53 
nitely small angles of diffraction; so that we can write :— 
a= (ce, — uy ) sin ao (ay — ay ) sin Ai, 
B=(8,—Bo) sin Bo= (21—Bo) sin A, 
¥=(%—Yo) sin HY =(%1 — Yo) Sin 3 
and 
cos” a) + cos” y+ cos’ y= 1, 
cos” a, + cos’ 8, + cos? y,=1. 
If in the penultimate equation we write 
ay=a,+(e—4)), Pyo=Pit+ (Lo-Fi), Y=n+(%—-MN1); 
and develop, we get 


Cosy; SIN Y1 (Yo—7Y1) = — COS a SiN ay (a4 — a) 
ae CUS B, sin By (Bo>—P1) 
aa Py COS iy cos By COS &y cos Bo 
COs 71 cos Yj} COS Y1 COS Yo 


Consequently y is a linear function of # and 8; hence, since 
according to our hypothesis p, and p; are constant, A depends 
only on a and 8. We write this, 
A? =; K?@(, 8). 
With the chosen position of the system of coordinates, the 
surface-elements that come into consideration are 


OF =p} 041081, Af=p5 0% 00; 


from these we get 
af, (8) end438,)3, 
P) 


and the amplitude of the diffracted light is 
Bes KW On, 06, P(4, 8). 


Therefore the kinetic energy of the same light incident upon the 
element Of, 


CA%p3 Da 0Bo= CK; pj 0a OAvP(a, BJO OT: - (0) 


Starting from this expression, we can further develop in 
two directions: the integration along 4,8, gives the energy 
incident upon the entire screen, which proceeds from OF; the 
integration along 4,8; gives the energy from the whole of the 
luminous surface F, falling on the element 9f. Let us carry 
out both operations. 

1. a, 8, are the variables; then 


: a= (a1—4a) sin ay, B=6,—6,, 


5a M. J. Frohlich on a new Proposition in the 
because in the above-mentioned position of the system of co- 


ordinates 8, and , are very nearly 5 5 


fol aa Ogi: ae 
oe sina, Cosy,’ 0h 
0% 0fo= on 0k 


Hence we get for the kinetic energy of the diffracted light 
proceeding from OF and falling upon the entire screen:— 


1 (te (+o __ | 
CK P3041 98: sey, | { D(a, B)oaodT. (1.) 


2. The variables are «,8,; then 
ae (a —4y) sin Bos B=B, 8, 
(for the same reason as before), 


oc . Oe 


SIN & COSY 


0f1=08, - 


ee 


hoe 0408. 
COS Yo 
Therefore the kinetic energy of the diffracted light proceeding 


from the entire luminous surface FF’, but falling only upon 
the element 0/, is 


1 +o ( to 
CRN ofa Dice | : { D(a, 8) 0# Of. (II.) 


The limits of the integration could be extended to —co and 
+c, since indeed ®(a, @) remains finite only when the values 
of a,—a,, Pi1—, are very small, but otherwise vanishes. 
Now, if we call the two elements OF and Of conjugate when 
their spherical angles in the aperture %§ are equal (conse- 
quently O0a,d08,=0«,08;, and thus expressions I. and II. 
become identical), -expressed in words this leads to the follow- 
ing proposition :-— ! 
The kinetic energy of the diffracted light emanating from a 
large, uniformly luminous spherical surface FF, and falling on 
the element Of of the screen, is equal to the kinetic energy of the 
diffracted light proceeding from the conjugate luminous element 
OF, and falling on the entire spherical surface of the screen ff 
—provided that the line joining the conjugate elements goes 


ca aie ats sh ROR RE BET 


Theory of Diffraction, and tts Application. 5d 


through the surface & of the aperture, or passes in its immediate 
vicinity, so that y,—y is extremely small*. 

We can at once avail ourselves of this result. 

Let us provisionally assume only that the kinetic energies 
of the incident and diffracted light are equal; then, if we take 
into account only the light emanating from 0%, out of expres- 
sion I. comes the following equation :— 


OR? Oa OPy iE Os 


= OW Co 0 foyer ane 


+n p@+0 
cand (_ P8)d88, 


from which 


+e { ae cos fe) 
He B\ hade = 2 (S206. 
. a, Rp3)J on OS 
To find, on the other hand, the intensity of the illumination in 
the element Of produced by the entire surface F¥, we have only 


to divide expression IT. by Cof=Cp2da, d6,, and we get the 
square of this amplitude, denoted by A, :— 


2 K? +o wo 4 
Aga ( (_ B(a, B) 3a dB. 


Cos Yo 


If we substitute in this equation the value of the double 
integral, and notice that y, and y, are very nearly equal, it 


becomes 
MN OP1 Sp 
ve yma 0 AE ss er Se 2 
a= Man 88 


in which §, signifies the other double integral. 

This is a remarkable result, and expresses that the tllumina- 
tion of the middle portion of the difraction-image of a very large 
uniformly luminous spherical surface is directly proportional to 
the area &, of the projection of the diffracting aperture upon the 
surface of the incident wave, but completely independent of the 
shape and position of the diffracting aperture. 

But we can with perfect justice invert this last train of 
thoughts and say:—If the proportionality to §, of this illu- 
mination is established, then the presumption from which this 
proportionality resulted is correct; or, the principle of the 


* I found this proposition at first for Fraunhofer’s phenomena only; 
on my communicating it by letter to Professor Réthy of Klausenberg, he 
pointed out that the proposition can also be extended to Fresnel’s phe- 
nomena. 


56 Ona new Proposition in the Theory of Diffraction. 


equality of the energies is proved as soon as this principle is 
verified for one of these apertures. 

The observations necessary for the purpose were carried out 
by the following method. In the vicinity of the focus of the 
collimator C C (fig. 2) was placed a portion of a spherical sur- 


Fig. 2. 
F 
ae ee 
\ Ni | ise Ne 
| D PALY 
V 2 
Cc He 
FE 


face F I’ made of fine paper oiled, the axis of symmetry of 
which feil into that of the collimator; behind EF F was a petro- 
leum-lamp burning with a large steady flame, which very 
equally illuminated the surface Ff F (the slight differences of 
intensity at its margin have no influence on the observation, 
since for these P(a, 6) already vanishes). The apparent mag- 
nitude of FF for the -middle of the collimator amounted to 
about 8°; therefore its dimensions were quite sufficient. 

In front of one of the half-lenses, H,, of a heliometer a 
square aperture was brought, and remained there during the 
entire observation ; before the other half-lens, H,, plane- and 
space-apertures were consecutively fixed, of the most varied 
shapes, as well as consisting some of one and others of a plu- 
rality of parts, and their dimensions and position were accu- 
rately determined. Both the half-lenses remained fixed during 
the observation ; and their axes coincided exactly with that 
of CC. 

- Before the focus of the heliometer the rotating Nicol, N,, 
polarized the diffracted light ; and the circular diaphragm o,, 
placed in the focus of the ocular, permitted only the middle 
part of the diffraction image to be observed, while the parallel- 
plane glass plate P, inclined 45° to the axis of the tube, 
reflected the image of the small circular aperture o,, exactly in 
such a way that o, and the image of 0,, in the ocular stood in 
immediate juxtaposition. The second Nicol, N.2, placed before 
the ocular, retained its position unaltered during the obser- 
vation. 

In the observation properly so called, one half-lens of the 
heliometer was covered and the other left uncovered; and 
now N, was rotated until the images of 0, and 0,, visible in the 
ocular both possessed the same intensity ; the former half-lens 


On the Illumination of Lines of Molecular Pressure. 57 


was now uncovered, and the other covered, and by repeated 
rotation of N, the equality of intensity of o, and o,, restored. 
These two positions of N, gave the relative intensity of the 
illumination of o, in the first and in the second case. 

Now, as the equality of the kinetic energies for rectangular 
apertures had, in a previous investigation”, been demonstrated 
as actually existing, the present investigation needed only to 
be directed to the proportionality of the illumination in 0, 
to §,. 

There was found here, as after the above examination was 
already highly probable, an exact agreement, within the limits 
of errors of observation, between the theoretic conclusions and 
the results of observation. 

On the ground of these investigations we are justified in 
pronouncing it a proposition confirmed by experiment, that, 
when the diffraction-angles are small, whatever the shape of the 
aperture, the kinetic energy of the incident light is equal to the 
kinetic energy of the diffracted light. 


Phys. Inst. Univ. Budapest, 
June 15, 1878. 


VII. On the Illumination of Lines of Molecular Pressure, and 
the Trajectory of Molecules. By Witu1AM Crooxss, F.R.S., 
PEAC 3S. | 


[X? UCTION Spark through Rarefied Gases—Dark Space round 

the Negatwe Pole—The author has examined the dark space 
which appears round the negative pole of an ordinary vacuum- 
tube when the spark from an induction-coil is passed through it. 
He describes many experiments with different kinds of poles, a va- 
rying intensity of spark, and different gases, and arrives at the 
following propositions :— 

Iilumination of Lines of Molecular Pressure—a, Setting up an 

intense molecular vibration in a disk of metal by electrical means 
excites a molecular disturbance which affects the surface of the disk 
and the surrounding gas. With a dense gas, the disturbance ex- 
tends a short distance only from the metal; but as rarefaction 
continues, the layer of molecular disturbance increases in thickness. 
In air at a pressure of 0:078 millim. this molecular disturbance ex- 
tends for at least 8 millims. from the surface of the disk, forming 
an oblate spheroid around it. 
- 6. The diameter of this dark space varies with the exhaustion, 
with the kind of gas in which it is produced, with the temperature 
of the negative pole, and, in a slight degree, with the intensity of 
the spark. For equal degrees of exhaustion it is greatest in hy- 
drogen and least in carbonic acid, as compared with air. 


* Wiedemann’s Annalen, vol. ili. p. 568. 
+ Abstract of a paper read before the Royal Society, Dec. 5, 1878. 


58 Mr. W. Crookes on the Illumination of 


c. The shape and size of this dark space do not vary with the — 


distance separating the poles, nor (or only very slightly) with altera- 
tion of battery-power, nor with intensity of spark. When the 
power is great the brilliancy of the unoccupied parts of the tube 
overpowers the dark space, rendering it difficult of observation ; 
but, on careful scrutiny, it may still be seen unchanged in size; nor 
does it alter even when, with a very faint spark, it is scarcely 
visible. On still further reduction of the power it fades entirely 
away, but without change of form. 


The author describes numerous experiments, Aevised to ascertain 


if this visible layer of molecular disturbance is identical with the 
invisible layer of molecular pressure or stress, the investigation of 
which has occupied him for some years. 

The Electrical Radiometer.—One of these experiments is as fol- 
lows:—An ordinary radiometer is made, with aluminium disks for 
vanes, each disk coated with a film of mica. ‘The fly is supported 
by a hard steel cup instead of a glass cup ; and the needle-pomnt on 
which it works is connected by means of a wire with a platinum 
terminal sealed into the glass; at the top of the radiometer-bulb 
a second terminal is sealed in. The radiometer can therefore be 
connected with an induction-coil, the movable fly being made the 
negative pole. 

Passing over the phenomena observed at low exhaustions, the 
author finds that, when connected with the coil, a halo of a velvety 
violet light forms on the metallic side of the vanes, the mica side 
remaining dark throughout these experiments. As the pressure 
diminishes, a dark space is seen to separate the violet halo from the 
metal. Ata pressure of half a millim. this dark space extends to 
the glass, and positive rotation commences. 

On continuing the exhaustion, the dark space further widens out 
and appears to flatten itself against the glass, and the rotation be- 
comes very rapid. 

When aluminium cups are used for the vanes instead of disks 
backed with mica, similar appearances are seen. The velvety violet 
halo forms over each side of the cup. On increasing the exhaus- 
tion the dark space widens out, retaining almost exactly the shape 
of the cup. The bright margin of the dark space becomes concen- 
trated at the concave side of the cup to a luminous focus, and widens 
out at the convex side. On further exhaustion, the dark space on 
the convex side touches the glass, when positive rotation commences, 
becoming very rapid as the dark space further increases in size and 
ultimately flattens against the glass. : 

Convergence of Molecular Rays to a Focus.—The subject next in- 
vestigated is the convergence of the lines of force to a focus, as 
observed with the aluminium cup. As this could not be accom- 
plished during rapid rotation, an instrument was made having the 
cup-shaped negative pole fixed instead of movable. On exhaustion, 
the convergence of the lines of force to a focus at the concave side 
was well observed. When the dark space is very much larger than 
the cup, it forms an irregular ellipsoid, drawn in towards the focal 


Lines of Molecular Pressure. 59 


point. Inside the luminous boundary a focus of dark violet light 
can be seen converging, and, as the rays diverge on the other side 
of the focus, spreading beyond the margin of the dark space—the 
whole appearance being strikingly similar to the rays of the sun 
reflected from a concave mirror through a foggy atmosphere. 

Green Phosphorescent Light of Molecular Impact.—At very high 
exhaustions the dark space becomes so large that it fills the tube. 
Careful scrutiny still shows the presence of the dark violet focus ; 
and the part of the glass on which fall the rays diverging from this 
focus shows a sharply defined spot of greenish-yellow light. On 
still further exhaustion, and especially if the cup is made positive, 
the whole bulb becomes beautifully illuminated with greenish-yellow 
phosphorescent light. 

This greenish-yellow phosphorescence, characteristic of high ex- 
haustions, is frequently spoken of in the paper. It must be remem- 
bered, however, that the particular colour is due to the special kind 
of soft German glass used. Other kinds of glass phosphoresce 
in a different colour. The phosphorescence takes place only under 
the influence of the negative pole. At an exhaustion of 4M* no 
light other than this is seen in the apparatus. At 0°9M the phos- 
phorescence is about at its maximum. When the exhaustion 
reaches 0°15 M, the spark has a difficulty in passing, and the green 
light appears occasionally in flashes only. At 0°06M the vacuum 
is almost non-conductive ; and a spark can be forced through only 
by increasing the intensity of the coil and well insulating the tube 
and wires leading to it. Beyond that exhaustion nothing has been 
observed. 

Focus of Molecular Force-—In an apparatus specially constructed 
for observing the position of the focus the author found that the 
focal point of the green phosphorescent light was at the centre of 
curvature, showing that the molecules by which it is produced are 
projected in a direction normal to the surface of the pole. Before 
reaching the best exhaustion for the green light, another focus of 
blue-violet light is observed ; this varies in position, getting fur- 
ther from the pole as the exhaustion increases. Jn the apparatus 
described, at an exhaustion of 19°3M, these two foci are seen 
simultaneously, the green being at the centre of curvature, while 
the blue focus is at nearly twice the distance. 

Nature of the Green Phosphorescent Light.—The author adduces 
the following characteristics of the green phosphorescent light, as 
distinguishing it from the ordinary light observed in vacuum-tubes 
at, lower exhaustions :— 

a. The green focus cannot be seen in the space of the tube, but 
where the projected beam strikes the glass only. 

b. The position of the positive pole in the tube makes scarcely 
any difference to the direction and intensity of the lines of force 
which produce the green light. The positive pole may be placed in 
the tube either at the extremity opposite the negative pole, or below 
it, or by its side. 

* M signifies the millionths of an atmosphere. 


60 Mr. W. Crookes on the Illumination of 


c. The spectrum of the green light is a continuous one, most of 
the red and the higher blue rays being absent ; while the spectrum 
of the light observed in the tube at lower exhaustions is character- 
istic of the residual gas. No difference can be detected by spec- 
trum-examination in the green light, whether the residual gas be 
nitrogen, hydrogen, or carbonic acid. 

d. The green phosphorescence commences at a different exhaus- 
tion in different gases. 

é. The viscosity of a gas is almost as persistent a characteristic 
of its individuality as its spectrum. The author refers to a preli- 
minary note and a diagram* of the variation of viscosity of air, 
hydrogen, and other gases at exhaustions between 240 M and 
0-1 M. From these and other unpublished results, the author 
finds that the viscosity of a gas undergoes very little diminution 
between atmospheric pressure and an exhaustion at which the green 
phosphorescence can be detected. When, however, the spectral 
and other characteristics of the gas begin to disappear, the viscosity 
also commences to decline ; and at an exhaustion at which the green 
phosphorescence is most brilliant the viscosity has rapidly sunk to 
an insignificant amount. 

f. The rays exciting green phosphorescence will not turn a corner 
in the slightest degree, but radiate from the negative pole in straight 
lines, casting strong and sharply defined shadows from objects which 
happen to be in their path. On the other hand, the ordinary lumi- 
nescence of vacuum-tubes will travel hither and thither along any 
number of curves and angles. 

Projection of Molecular Shadows.—The author next examines the 
phenomena of shadows cast by the green light. The best and 
sharpest shadows are cast by flat disks and not by narrow-pointed 
poles; no green light whatever is seen in the shadow itself, no 
matter how thin, or whatever may be the substance from which it 
is thrown. 

From these and other experiments, fully described in the paper, 
he ventures to advance the theory that the induction-spark actually 
illuminates the lines of molecular pressure caused by the electrical 
excitement of the negative pole. ‘The thickness of the dark space is 
the measure of the mean length of the path between successive col- 
lisions of the molecules. The extra velocity with which the mole- 
cules rebound from the excited negative pole keep back the more 
slowly moving molecules which are advancing towards that pole. 
The conflict occurs at the boundary of the dark space, where the 
luminous margin bears witness to the energy of the collisions. 

When the exhaustion is sufficiently high for the mean length of 
path between successive collisions to be greater than the distance 
between the fly and the glass, the swiftly moving rebounding mole- 
cules spend their force, in part or in whole, on the sides of the 
vessel, and the production of light is the consequence of this sudden 
arrest of velocity. The light actually proceeds from the glass, and 


* Proc. Roy. Soc. Noy. 16, 1876, vol. xxv. p. 305. 


sted 


ea. oe nn 


Lines of Molecular Pressure. 61 


is caused by fluorescence or phosphorescence on its surface. No 
light is produced by a mica or quartz screen; and the more fluo- 
rescent the material the better the luminosity. Here the consi- 
deration arises that the greenish-yellow light is an effect of the 
direct impact of the molecules in the same electrical state on the 
surface of the glass. The shadows are not optical, but are mole- 
cular shadows, revealed only by an ordinary illuminating effect ; 
this is proved by the sharpness of the shadow when projected from 
a wide pole. 

Phosphorescence of Thin Films.—An experiment is next described 
in which a film of uranium glass, sufficiently thin to show colours 
of thin plates, is placed in front of a thick plate of the same glass, 
the whole being enclosed in a tube with terminals and exhausted to 
a few millionths of an atmosphere. Of this the following observa- 
tions are recorded :— 

a. The uranium film, being next to the negative pole, casts a 
strong shadow on the plate. 

6. On making contact with the coil, the thin film flashes out 
suddenly all over its surface with a yellowish phosphorescence, 
which, however, instantly disappears. The uncovered part of the 
plate does not become phosphorescent quite suddenly, but the phos- 
phorescence is permanent as long as the coil is kept at work. 

c. With an exceedingly faint spark the film remains more lumi- 
nous than the plate; but on intensifying the spark, the luminosity 
of the film sinks, and that of the uncovered part of the plate 
increases. 

d. If a single intense spark be suddenly sent through the tube, 
the film becomes very luminous, while the plate remains dark. 

These experiments are conclusive against the phosphorescence 
being an effect of the radiation of the phosphorogenic ultra-violet 
light from a thin layer of arrested molecules at the surface of the 
glass ; for were this the case, the film could under no circum- 
stances be superior to the plate. 

The momentary phosphorescence and rapid fading of the film 
prove more than this. The molecular bombardment is too much 
for the thin film. It responds thereto at first, but immediately 
gets heated by the impacts, and then ceases to be luminous. The 
plate, however, being thick, bears the hammering without growing 
hot enough to lose its power of phosphorescing. 

Mechanical Action of Projected Molecules.—W hen the coil was first 
turned on, the thin film was driven back at the moment of becoming 
phosphorescent, showing that an actual material blow had been 
given by the molecules. Experiments are next described in which 
this mechanical action is rendered more evident. A small rotating 
fly, capable of being moved about in any part of an exhausted bulb, 
is used as an indicator; and by appropriate means the molecular 
shadow of an aluminium plate is projected along the bulb. Whether 
entirely in or entirely out of the shadow, the indicator scarcely 
moves ; but when immersed so that one half is exposed to molecular 
impact, the fly rotates with extreme velocity. 


62 Mr. W. Crookes on the Illumination of 


Magnetic Deflection of Lines of Molecular Force-—With this ap- 
paratus another phenomenon was investigated. . It is found that 
the stream of molecules whose impact on the glass occasions evo- 
lution of light is very sensitive to magnetic influence ; and by bring- 
ing one pole of an electromagnet, or even .of a small permanent 
magnet, near, the shadow can be twisted to the right or to the left. 

When the little indicator was placed entirely within the mole- 
cular shadow no movement was produced. As soon, however, as 
an adjacent electromagnet was excited, the shadow was twisted half 
off the indicator, which immediately rotated with great speed. 

The Trajectory of Molecules—The amount of deflection of the 
stream of molecules forming a shadow is in proportion to the mag- 
netic power employed. 

The trajectory of the molecules forming the shadow is curved 
when under the magnetic influence: the action of the magnet is to 
twist the trajectory of the molecules round in a direction at an 
angle to their free path, and to a-greater extent as they are nearer 
the magnet, the direction of twist being that of the electric current 
passing round the electromagnet. 

Laws of Magnetic Deflection—An apparatus was constructed so 
that the deflection of a spot of light was used instead of that of a 
sbadow, a horseshoe magnet being placed underneath the negative 
pole to deflect the trajectory. The action cf the north pole being 
to give the line of molecules a spiral twist one way, and that of 
the south pole being to twist it the other way, the two poles side 
by side compel the line to move in a straight line up or down, 
along a plane at right angles to the plane of the magnet and a line 
joining its poles. 

The ray of molecules does not appear to obey Ampére’s law, as 
it would were it a perfectly flexible conductor, joining the negative 
and the positive pole. The molecules are projected from the nega- 
tive ; but the position of the positive pole—whether in front, at the 
side, or even behind the negative pole—has no influence on their 
subsequent behaviour, either in producing phosphorescence, or 
mechanical effects, or in their magnetic deflection. The magnet 


gives their line of path a spiral twist, greater or less according to 


its power, but diminishing as the molecules get further off. 

Numerous experiments were tried in this apparatus with different 
gases, and with the magnet in and out of position. 

Working with exhausted air it was found that the spot of green 
phosphorescence on the screen is visible at an exhaustion of 
102°6 millim., when the mean free path of the molecules, measured 
by the thickness of the dark space round the negative pole, is only 
12 millims. Henceit follows that a number of molecules sufficient 
to excite green phosphorescence on the screen are projected the 
whole distance from the pole to the screen, or 102 millims., with- 
out being stopped by collisions. 

Alteration of Molecular Velocity.—lIf we suppose the magnet to 
be permanently in position, and thus to exert a uniform downward 
pull on the molecules, we perceive that their trajectory is much 


Lee 


~ et i a a 


Lines of Molecular Pressure. 63 


curved at low exhaustions, and gets flatter as the exhaustion in- 
creases. A flatter trajectory corresponds to a higher velocity. 
This may arise from one of two conditions: either the initial im- 
pulse given by the negative pole is stronger, or the resisting medium 
is rarer. The latter is probably the true one. The molecules 
which produce the green phosphorescence must be looked upon as 
in a state differing from those arrested by frequent collisions. 
The latter impede the velocity of the free molecules and allow 
longer time for magnetism to act on them; for, although the de- 
flecting force of magnetism might be expected to increase with the 
velocity of the molecules, Prof. Stokes has pointed out that it 
would have to increase as the square of the velocity, in order that 
the deflection should be as great at high as at low velocities. 

Comparing the free molecules to cannon-balls, the magnetic 
pull to the earth’s gravitation, and the electrical excitation of the 
negative pole to the explosion of the powder in the gun, the tra- 
jectory will be flat when no gravitation acts, and curved when 
uuder the influence of gravitation. It is also much curved when 
the ball passes through a dense resisting medium ; it is less curved 
when the resisting medium gets rarer; and, as already shown, 
intensifying the induction spark, equivalent to increasing the 
charge of powder, gives greater initial velocity, and therefore 
flattens the trajectory. The parallelism is still closer if we com- 
pare the evolution of light seen when the shot strikes the target, 
with the phosphorescence on the glass screen from molecular 
impacts. 

Focus of Heat of Molecular Impact.—The author finally describes 
an apparatus in which he shows that great heat is evolved when 
the concentrated focus of rays from a nearly hemispherical alumi- 
nium cup is deflected sideways, to the walls of the glass tube, by a 
magnet. By using a somewhat larger hemisphere, and allowing 
the negative focus to fall on a strip of platinum-foil, the heat rises 
to the melting-point of platinum. 

An Ulira-gaseous State of Matter—The paper concludes with 
some theoretical speculations on the state in which the matter 
exists in these highly-exhausted vessels. The modern idea of the 
gaseous state is based upon the supposition that a given space 
contains millions of millions of molecules in rapid movement in all 
directions, each having millions of encounters in a second. In 
such a case, the length of the mean free path of the molecules is 
exceedingly small as compared with the dimensions of the vessel, 
and the properties which constitute the ordinary gaseous state of 
matter, which depend upon constant collisions, are observed. But 
by great rarefaction the free path is made so long that the hits in 
a given time may be disregarded in comparison with the misses, in 
which case the average molecule is allowed to obey its own motions 
or laws. without interference ; and if the mean free path is com- 
parable to the dimensions of the vessel, the properties which con- 
stitute gaseity are reduced to a minimum, and the matter becomes 
exalted to an ultra-gaseous state, in which the very decided but 


64 Notices respecting New Books. 


hitherto masked properties now under investigation come into 

lay. . 
: cine of Molecular Light.—In speaking of a ray of molecular 
light the author has been guided more by a desire for conciseness 
of expression than by a wish to advance a novel theory. But he 
believes that the comparison, under these special circumstances, is 
strictly correct, and that he is as well entitled to speak of a ray of 
molecular or emissive light when its presence is detected only by 
the light evolved when it falls on a suitable screen, as he is to speak 
of a sunbeam in a darkened room as a ray of vibratory or ordinary 
light when its presence is to be seen only by interposing an opaque 
body in its path. In each case the invisible line of force is spoken 
of as a ray of light; and if custom has sanctioned this as applied 
to the undulatory theory, it cannot be wrong to apply the expres- 
sion to emissive light. The term emissive light must, however, be 
restricted to the rays between the negative pole and the luminous 
screen ; the light by which the eye then sees the screen is, of 
course, undulatory. 

The phenomena in these exhausted tubes reveal to physical 
science a new world—a world where matter exists in a fourth 
state, where the corpuscular theory of light holds good, and where 
light does not always move in a straight line—but where we can 
never enter, and in which we must be content to observe and ex- 
periment from the outside. 


VIII. Notices respecting New Books. 


I. Report on the Administration of the Meteorological Department of 
the Government of India im 1876-77. 

Il. Report on the Meteorology of India in 1876. By Hunry F. 
BuanForD, Meteorological Reporter to the Government of India. 
Second Year. Calcutta, 1878. . 

IU. Indian Meteorological Memows. Published by order of His 
Excellency the Viceroy and Governor General of India im Council, 
under the Direction of Henry I’. Buanrory, Meteorological Re- 
porter to the Government of India. Calcutta, 1878. 


Ls publications make us acquainted with the progress of me- 

teorological work in India during the year 1876, under the able 
superintendence of Mr. Blanford. From them we learn that the 
system of Meteorological Observation, the administration of which 
was concentrated by order of the Government in a single central 
office, has not only worked well, but that the area over which it 
now extends embraces 43° 30’ of longitude and 24° of latitude ; viz. 
from 51° to 94° 30’ of east longitude, and from 10° to 34° of north 
latitude. 

For many years the pursuit of meteorology consisted in obser- 
ving the indications of the instruments at certain periods of the 
day, and deducing from the readings thus obtained the mean tem- 
perature or pressure at these periods; but of late years a much 


Geological Society. 65 


‘more scientific method has obtained. Excellent as many of these 


observations were, furnishing, as in Howard’s case, the elements of 
climate, they were still isolated; for while they recorded weather- 
changes, it was only at the particular localities where they were ob- 
served. For real advancement a network of stations was requisite : 
to organize such a network was clearly out of the power of isolated 
observers ; only large Associations could undertake a work of the 
kind ; and even under the auspices of an old-established association, 
such an undertaking might lack the necessary stability in order 
to carry it out toa useful end. Governments alone could really 
grapple with such an extensive subject as is presented to us in me- 
teorology ; and this has been accomplished by both the American 
and Indian Governments. In India many important questions, 
bearing in no small degree on the welfare and even the lives of the 
inhabitants, have arisen in consequence of the widespread calamities 
with which the peninsula has been visited, particularly the recent 
famines. To such questions Mr. Blanford, the Meteorological 
Reporter to the Government of India, has directed his most sedu- 
lous attention, and has sought to elucidate the links of the chain of 
causation which led to and culminated in the famine of 1876. Two 
of these links have been ascertained—one to consist of the failure 
of rainfall in the western and southern provinces, where the staple 
vegetation was withered to the condition of hay under an ever 
cloudless sky, the other of a superabundant outpour over the Bur- 
mese peninsula and the Bay of Bengal of the rain withheld from 
the Provinces, which overcharged the Irawadi and caused those dis- 
astrous floods that washed away and drowned the rice crops: thus 
the famine was brought about by a failure and an excess of rainfall— 
the failure being largely attributable to the prevalence of northerly 
and north-westerly land winds, and the excess to a vapour-laden 
current from the south-west, which, recurving cyclonically around 
the Bay of Bengal, discharged its burden over the Bay and on the 
south-east coast of the peninsula. 

This second report of the Department of Indian Meteorology is 
an admirable specimen of the work effected by the Indian Govern- 
ment. 


IX. Proceedings of Learned Societies. 


GEOLOGICAL SOCIETY. 
[Continued from vol. vi. p. 313.] 
November 20, 1878.—R. Etheridge, Esq., F.R.S., 
Vice-President, in the Chair. 


re following communications were read :— 

1. “On the Upper-Greensand Coral Fauna of Haldon, Devon- 
shire.” By Prof. P. Martin Duncan, M.B. Lond., F.R.S., F.G.S., 
&e. 


Phil. Mag. 8. 5. Vol. 7. No. 40. Jan. 1879. iy 


66 Geological Soviety 


2. “Notes on Pleurodon affinis, sp. ined., Agassiz, and Description 
of three spines of Cestracionts from the Lower Coal-measures.” - 


J. W. Davis, Esq., F.G.S. 


3. “On the Distribution of Boulders by other Agencies than that 
of Icebergs.” By C. E. Austin, Esq., C.E., F.G.S. 

The author is of opinion that if boulders had been distributed by 
floating ice they should now be accumulated ‘‘ in certain parallel and 
quasi-concentric lines.” This he does not find to be the case in 
Sweden and North Russia, where the distribution is irregular. 


From the mode of distribution he infers that the boulders must have — 


been uniformly distributed in the ice blocks, whereas they ought to 
have been most abundant at the base. The boulders are not con- 
nected with existing ravines, and the author does not see how ice 
can move on a plain. He has never seen a glacier-moraine, but 
thinks that these boulders are not like the blocks in moraines. In 
Siberia, Portugal, and Rio Janeiro the author has seen solid nuclei 
in decomposed granite. Such boulders, as he notices, may be left 
after decomposition of a once flowing molten mass, of which they 
have formed a part or in which they have been entangled. 


December 4.—Henry Clifton Sorby, Esq., F.R.S., President, 
in the Chair. 


The following communications were read :— 

1. “On some Mica-Traps from the Kendal and Sedbergh Dis- 
tricts.” By Prof. T. G. Bonney, M.A., FLR.S., E-Gis., and 
S. Houghton, Hsq., B.A. ° 


The rocks described by the authors are mapped by the Geo- 


logical Survey on quarter sheets 98 N.E., 98 S.E., and 97 N.W., 
and in parts briefly mentioned in the accompanying memoirs, 
under the generic name mica-trap. Seventeen examples are de- 
scribed macroscopically and microscopically ; and of eight, chemical 
analyses are given. It appears better to call one a porphyrite and 
two diorites (micaceous varieties). ‘The remainder are all cha- 
racterized by abundance of mica (biotite). Augite also appears to 
have been generally a constituent; but it has almost invariably been 
replaced by secondary products—calcite, dolomite, viridite, &c. Three 
are crystalline in structure; one of these is named minette, the 
others kersantite. ‘The remaining eleven show a microcrystalline or 
cryptocrystalline base. It is proposed to call eight of them minette- 
felsite, the rest kersantite-porphyrite. These rocks commonly occur 
in rather narrow dykes; they are intrusive in Silurian strata, and, 
in the authors’ opinion, are undoubtedly true igneous rocks. 


2. “ Pleistocene Notes on the Cornish Coast near Padstow.” By 
W. A. E. Ussher, Esq., F.G.S. 

In this paper the author described certain deposits seen in a small 
bay near St. Enodock’s chapel, and known as Daymer Bay, and in 
section at Greenway cliffs. The former included a portion of raised 
beach, and a reef of consolidated old beach and a peaty deposit belew 


sO alii 


_ ee ee ed raed: re a oe 


Intelligence and Miscellaneous Articles. 67 


high-water mark, the raised beach indicating a depression of from 
5 to 10 feet and a subsequent elevation of more than that amount, 
during a pause in which the lower beach was formed. The further 
elevation of the coast was sufficient to favour the growth of forests 
furnishing the peaty bed, which a subsequent subsidence has brought 
down to its present level. Greenway cliffs consist of grey slates, 
resting against which, in two places, are old consolidated blown 
sands; about 5 feet above high-water mark is a raised beach, near 
which the face of the cliff consists of ‘‘ head” capped by gravel. 
The author discussed the relative ages of these deposits, and in- 
clined to regard the gravel as a fluviatile deposit, and the stony 
loam or ‘“‘ head” as an ancient talus or flood-gravel, both deposited 
before the raised beach. 


3. The Pleistocene History of Cornwall.” By W. A. E. Ussher, 
Esq., F.G.S. 

In the first part of this paper the author, from his own observa- 
tions and the writings of other geologists, gave detailed descriptions 
of the various superficial deposits of Cornwall as exposed in nume- 
rous coast-sections. 

In the second part he discussed the relative ages of these deposits, 
for which he proposed the following classification :— 

1. The oldest beds described are patches of quartzose gravel, 
found up to 400 feet above the present sea-level ; these are regarded 
by the author as of fluviatile origin, and as being possibly redeposited 
Tertiary beds. Their age may be any thing between Cretaceous 
and Glacial. 

2. Boulder-gravels, from 40 to 50 feet above sea-level. 

3. Raised beaches, up to 15 feet above sea-level. 

4. Old blown sand closely associated with the raised beaches. 

5. “Head” or talus of angular fragments lying upon the raised 
beaches, and therefore of younger date than the latter. 

6. Stream-tin gravels, evidently older than the forest stratum. 

7. Submerged forests, evidently occupying a long period subse- 
quent to the deposition of the stream-tin gravels. 

8. Recent marine and fluviatile deposits. 

In conclusion he remarked on the paucity of superficial deposits 
in Cornwall, the absence of evidence of glacial conditions, and the ~ 
proofs of great changes in the level of the area. 


X. Intelligence and Miscellaneous Articles. 


ON THE FIGURE OF THE PLANET MARS. 
LETTER FROM PROFESSOR H. HENNESSY. 


M A MIGUES published in 1874, in the Comptes Rendus of 

~ the Academy (vol. lxxvii. p. 1556), « memorandum 
on the Configuration of the planet Mars, which seems to me to 
verify completely some results at which I arrived some time ago. 
The author says :— 


68 Intelligence and Miscellaneous Articles. 


“T propose in this memorandum to remove this objection [namely, 
the objection to the hypothesis of the original fluidity of the planets 
on the ground of the exceptional magnitude of the oblateness of the 
planet Mars] by showing that geometers have not handled the pro- 
blem of spheroids in such a general way as could be wished.” And 
after having indicated the method he employs, he says :—‘‘ This 
calculation, made by the usual methods (that is to say, by employing 
Laplace’s functions and neglecting quantities of the second order), 
leads me to the results which follow.” . 

Relatively to these points, | may be permitted to remark that I 
have long ago investigated the same problem of spheroidal attrac- 
tions and by precisely the same methods—that is, by the applica- 
tion of Laplace’s functions. At first I applied the result of my 
calculations to the question of the figure of the Earth, with the aim 
of thoroughly studying the theory which endeavours to explain its 
spheroidal form by the attrition of its surface. This theory was 
at first proposed by Playfair in his ‘ Illustrations of the Huttonian* . 
System ;’? and it has been put forward afresh by Sir John Herschel 
in his ‘Outlines of Astronomy.’ It also acquires some interest 
because it has been cited by Sir Charles Lyell and serves as a foun- 
dation for the opinion which he maintains in his ‘ Principles of 
Geology,’ as to the earth’s figure. 

The results which I have obtained show that this theory cannot 
be upheld; for the greatest ellipticity which the earth could possess 
from the action of attrition cannot exceed 37, a fraction which 
differs considerably from that which is usually admitted as the 
result of observations. 

In 1864 I had for the first time applied my calculations to the 
question of Mars, in a communication to the British Association ; 
and a short extract of my paper was published. 

In February 1870 I published a memoir in ‘ Atlantis’ (No. ix., 
8vo, London, February 1870) on the Configuration of the Planet 
Mars; and I applied to Mars the mathematical results of my pre- 
vious investigations. J found (p. 178) an equation giving the 
ellipticity as a function of the mean density D’ and of the surface- 
density D of the planet, 


: 5g q 
D 3D’ 
1023652 18 Df eas 
°D ( 5 D 


In the equation q is the ratio of the centrifugal force to gravity. 
Now, if we employ the notation of M. Amigues, q will be replaced 

by ¢, and D’ by p’, and D by p, which gives 

Te ? 


Sa Mapes FOS 
10 263 2( pero 0 

es, p \ p 

a formula which is precisely that given by M. Amigues. 


* In the Comptes Rendus “ Hutton ” is misprinted “ Newton.” 


Intelligence and Miscellaneous Articles. 69 


I have also deduced from my formula this conclusion—that if 
the greatst oblateness sometimes attributed to Mars be admitted, 
we must conclude that its surface-density is greater than the inte- 
rior density of the planet; but as such a conclusion seems to me to 
be contrary to the laws of Physics, if the constitution of Mars be 
like that of the Earth, until more complete observations shall 
have been made, I prefer accepting the conclusions of Bessel, 
Johnson, Oudemans, and Winnecke, who admit an almost sensible 
oblateness for Mars. 

An extract from my previous researches on the theory of the 
form of the Earth as a result of attrition appeared in several scien- 
tific journals some years ago; I am sure, however, that the results 
got by M. Amigues were obtained in a manner altogether indepen- 
dent of, and without his having had any knowledge of my investi- 
gations. 

The entire agreement of his calculations with those I had pre- 
viously made is not only interesting as far as regards Mars, but they 
confirm the idea I had formerly upheld in opposition to the theory 
of Playfair, Herschel, and Lyell, on the form and structure of the 
Earth.— Comptes Rendus de (Académie des Sciences, No. 17, Oct. 22, 
1878. 


ON A NEW PHENOMENON OF STATIC ELECTRICITY. 
BY E. DUTER. 


I have the honour of submitting to the Academy the description 
of an experiment which proves that, in certain cases, electrization 
changes the volume of bodies. 

In order to make the experiment, we procure a large thermo- 
meter-case. With this we make a condenser of which it is the 
insulator by passing into its interior a platinum wire, filling it 
with water, and pasting to its outer surface a sheet of tinfoil. We 
have thus a Leyden jar, which we charge by the usual methods. 
As soon as it receives the charge the surface of the water is seen to 
sink, remain stationary as long as the charge continues, and in- 
stantly resumes its former level with the discharge. As in a con- 
denser the electricity resides only in the insulator, it is natural to 
conclude from this experiment that the glass dilates. We obtain a 
first confirmation of this idea on remarking that, whatever may be 
the nature of the armatures—tinfoil, water, saline solutions, or 
mercury—the same apparent contraction of the liquid inside is ob- 
served. ‘T'o remove all doubt, I modified the apparatus by putting 
the Leyden jar into a closed glass case, terminated also with a ther- 
mometric stem, and likewise filled with a conducting liquid. In 
this arrangement the liquid of the inner reservoir forms the internal 
armature of the condenser, the liquid in the case forms the external 
armature, and the surface of the inner glass is the insulator. It is 
this which, if our previsions are correct, should be enlarged by the 
electrization. We find, in fact, that the water descends in the ther- 
mometric tube of the inner vessel, and a sensibly equal quantity 
ascends in the measuring-tube of the outer case. As soon as the 


70 Intelligence and Miscellaneous Articles. 


apparatus is discharged, every thing returns to the initial state: 
the liquid which had descended in the tube of the inner vessel rises 
again; and that which had risen in the tube of the outer case re- 
descends. We must therefore conclude that the internal capacity 
and the external volume increase during the charge of a Leyden jar. 

To leave no doubt on the subject, I will review the objections 
which can be made to this conclusion. 

(1) The effect cannot be attributed to a rise of temperature, 
since the discharge causes it to disappear immediately instead of 
increasing it. 

(2) Electric pressure might be suggested as the cause; but that 
would be the same on both faces of the dielectric, and then it would 
produce a diminution of volume instead of the increase observed. 

(3) It might also be said that the liquid does not perfectly wet 
the glass before the electrization, and that afterwards, in conse- 


quence of attraction, more intimate contact is produced, giving rise 


to an apparent contraction of the liquid. But then the same phe- 
nomenon ought to be produced for the exterior liquid—which does 
not take place. 

(4) Again, different properties of the positive and negative ar- 
matures might be mentioned. But if the communications of the 
apparatus with the electrical machine be reversed, the direction of 
the phenomenon does not change. 

In short, it is established that, ina Leyden jar, the insulator un- 
dergoes, through the electrization, a dilatation which can neither be 
accounted for by a rise of temperature nor by an electric pressure. 
We therefore find ourselves in the presence of a new phenomenon; 
as to the interpretation that may be given of it, although several 
ey themselves to the mind, it would be premature to discuss 
them. 


M. Jamin, in presenting the above Note to the Academy, was 
anxious to acknowledge that, ten years since, M. Govi had made, and 
published in the Actes de l Acudémie de Turin, the first part of the 
experiments of M. Duter. M. Govi observed thatthe internal volume 
seems to increase during the charging of a Levden jar; and he 
attributed this effect to a contraction of the liquid which it con- 
tains; but he did not institute any experiment to show that the 
external volume is augmented. This is what M. Duter has done; and 
it has led him to a conclusion contrary to that of M. Govi—namely, 
that the effect observed is simply due to a dilatation of the dielec- 
tric case.—Comptes Rendus de (Académie des Sciences, Nov. 23, 
1878, tome Ixxxvil. pp. 828-830. 


NEW OBSERVATIONS ON THE PART PLAYED BY PRESSURE IN 
CHEMICAL PHENOMENA. BY M. BERTHELOT. 
Permit me to call attention to a circumstance in the remarkable 
experiments of M. Pictet on the liquefaction of oxygen and hydro- 
gen. Perhaps it will not be uninteresting to remark that the 


| 


Intelligence and Miscellaneous Articles. 71 


decomposition of chlorate of potassium into oxygen and chloride of 
potassium, an eawothermic reaction, and not limited by ats inverse, is 


not arrested by a pressure of 320 atmospheres. In fact, from my 


measurements, the reaction 


| ClO,K=KCIl+ 0, 
would liberate at the ordinary temperature +11°0. At about 400°, 
the chlorate being fused and the chloride solid, the amount libera- 
ted could not but be augmented. 

It is the same with the decomposition of formate by hydrate ‘of 
potass, the hydrogen continuing to be liberated even under a pres- 
sure of more than 600 atmospheres. Here, again, is an exothermic 
reaction not limited by its inverse. In fact the transformation of 
the system C,HKO,+KHO, into C,0,K,+ H, would liberate at the 


ordinary temperature 


277°8— 259'4=18°4 calories. 
At about 400°-500°, all the substances being supposed to be fused, 
the heat disengaged would not be much modified ; for the heats of 
fusion of the known salts but little exceed +4 calories, and the 
initial system comprises 2 fused molecules, the final system con- 
taining only 1. ; 

Thus the exothermic reactions persist, whatever may be the 
amount of the pressure. It is nevertheless probable that the velo- 
city of such a reaction is changed, and perhaps also the temperature 
at which it is effected; but the reaction itself does not cease to 
take place. This is a fresh proof in support of the opinions 
enunciated by the author of the present note, on a question so im- 
portant to mechanical chemistry—opinions contested at first, but 
which derive fresh support from every new observation *.— Annales 
de Chimie et de Physique, October 1878, tome xv. p. 149. 


ON AN AUTOMATIC CURRENT-REGULATOR. BY M. HOSPITALIER. 


The apparatus which we have the honour to present to the Aca- 
demy is composed of aresistance-coil wound in one layer only, the wire 
of which has been denuded along a generatrix of the spiral over a 
width of about 1 centimetre. A lever, somewhat convex, and formin g 
a divider, is applied to the denuded part of the wire. This divider 
is attached at one of its extremities to an armature placed before an 
electro-magnet, in which the current circulates which is to be 
regulated. An antagonizing spring supports the lever at its other 
extremity. The circuit is formed by the resistance-coil, the lever 
and the electromagnet. The apparatus being regulated fora eee. 
mined intensity, the divider introduces into the circuit a certain 
number of turns of the coil. Jf the current increases in intensity 
the electromagnet attracts its armature more strongly, the divider 
shifts its fulerum and introduces into the circuit a ereater number 

* See Chimie organique fondée sur la Synthese, t. ii. p. : 
Annales de Chimie ie Phe 3° sér. t. fai 4 41 59, ‘levi 
p- 239, and especially 4° série, t. xviii. p. 95, and 5¢ série, t. xii. p. 310, &e. 


72 Intelligence and Miscellaneous Articles. 


of turns of the coil; the resistance increases, and the intensity is 
diminished. ‘The opposite effect is produced if the intensity of the 
current diminishes. 

By suitably regulating the force of the antagonizing spring, the 
electromagnet, the distribution of the wire upon the bobbin, and 
the curvature of the divider, we can render the system astatic; and 
then the apparatus gives a mathematically constant current. 

In practice we can ‘maintain the intensity of the current between 
two limits fixed beforehand, and as close as we will. 

From an industrial point of view, the apparatus can be applied 
to electrotyping, to the incandescence of wires of platmum or 
iridium (to prevent their fusion), and, if the problem should one 
day receive its practical solution, to the distribution of electricity 
in dwelling-houses, where the apparatus will play the part of a 
real meter and divider of the electric current.—Comptes Rendus de 
V Académie des Sciences, Dec. 9, 1878, t. lxxxvil. p. 920. 


ON THE PHYSICAL STATE OF CENTRAL EUROPE IN THE TERTIARY 
PERIOD (AS DISPLAYED IN THE WRITINGS OF PROF. 0. HEER). 
BY M. VAN TIEGHEM. 


By publishing, in 1828, his Histoire des Végétaux fossiles, M. 
Ad. Brongniart laid the foundation of vegetable palzontology. 
Having a few years afterwards, about 1835, entered upon the new 
path, M. Oswald Heer was not long in gaining therein one of the 
highest ranks, which he has been able to keep. 

The study of the plants, and also of the insects, of the Tertiary 
formations had till then been much neglected; and it was to these 
that Prof. Heer almost exclusively devoted the fine series of in- 
vestigations which he indefatigably pursued for more than forty 
years. 

" By a great number of special memoirs, published in succession 
from 1836 to 1858, he applied himself first to making known the 
plants and insects observed in the three horizons of the Miocene 
in different localities in Switzerland. Among the local floras and 
faunas thus established, unquestionably the richest, and also the 
most instructive, is that of the lignites of Ciningen, belonging to 
the Upper Miocene, and comprising 475 species of plants. Having 
accomplished this, he compared and coordinated the rich material 
thus acquired for science in two great works forming a whole :— 
the Faune des Insectes tertiaires, of which I have not to speak here ; 
and the Flore tertiatwre de la Suisse, in which are described, figured, 
and classified 920 species of fossil plants, of which 700 were new. 

A little later, completing his investigation of the Miocene plants 
of Switzerland, extending his researches to the vegetables of all the 
tertiary formations of Europe, and adding the results obtained 
respecting the plants of the same age found in the other regions 
of the globe, he endeavoured to reconstruct the world of which 
those creatures formed a part, and gave us his grand work entitled 
Recherches sur le Climat et la Végétation du Pays tertiaire, a French 


Intelligence and Miscelianeous Articles. 73 


edition of which was published in 1861. Since that period, pur- 
suing without intermission the study of the Tertiary plants dis- 
covered in divers countries till then unexplored (for example, the 
Isle of Wight, Greenland, &c.), he laboured incessantly, adding 
some general features to the magnificent work to a sketch of which 
we here limit ourselves. 

Let us first place ourselves in Switzerland, where, as we know, 
the various freshwater formations belong to the three horizons of 
the Miocene. The Tertiary flora of Switzerland comprised at 
least 3000 species of plants. It was consequently much richer 
and more varied than even that of the most favoured countries of 


‘the south of Europe; and we must go into tropical regions—to 


Jamaica, for instance, and to Bahia—to see at the present time 
such an abundance and diversity of forms. Assembled at that 
time within the little territory of Switzerland, those plants are 
now disseminated into all parts of the world; but itis in America, 
and especially in the southern United States, that most of them 
are at present found. If, instead of the number of species, we 
consider the mass of the vegetation, Miocene Switzerland still less 
resembles the present Europe, and comes nearest to America by its 
abundance of evergreen oaks, maples, and poplars, by its plane- 
trees, liquidambars, Robinic, Sequoiee, Taxodia, and ternate-leaved 
pines—to Japan by its Camphor e and Glyptostrobi, and, lastly, to 
the Atlantic islands byits laurels. It has nevertheless a character 
peculiar to itself, which is now found nowhere on the surface of 
the globe—a character expressed at the same time in that singular 
combination of specific types al present separated by great 
distances, and by the existence of certain very peculiar species 
which have become extinct. 

From Switzerland let us pass to Europe, in order to compare 
the characters of the flora in the various successive Tertiary for- 
mations. We shall there see striking differences, which impressed 
a peculiar physiognomy on the vegetation of each period. Thus, 
in the Hecene flora Indo-Australian types predominate, the 
American species being but very feebly represented, and the cha- 
racteristic plants of the temperate zone totally wanting. The 
Hocene flora was therefore essentially tropical. 

The flora of the Lower Miocene has a subtropical character— 
though tropical forms are still numerous, and the Indo-Australian 
types still play an important part. The generality of the species, 
however, belong at the present time to the subtropical and warm 
zones ; and, above all, the forms of temperate climates are seen to 
make their appearance there. Besides, both the subtropical and 
the temperate forms correspond with American types, and give to 
the flora an American tint. 

At the period of the Upper Miocene the tropical types have not 
yet disappeared ; but they are reduced to about 7 per cent. of the 
total vegetation, while those of the temperate zone rise to 18 per 
cent. The forms of the subtropical and warm regions still pre- 
dominate. The American character of the vegetation i is expressed 
still more plainly and evidently. 


Phil. Mag. 8. 5. Vol. 7. No. 40. Jan. 1879. G 


74. Intelligence and Miscellaneous Articles. 


In the Pliocene flora the tropical types have totally disappeared ; 
but a few subtropical species are still found. The plants of the 
warm region predominate; those of the temperate zone continue 
to increase in number. The American character remains very 
marked. 

Finally, in the Quaternary flora the subtropical species and 
those of the warm region have entirely disappeared, even in Italy. 
Most of the plants are identical with those now living in the same 
regions. Some exotic and extinct types, however, are found in it, 
and as it were an echo of America. 

We see, then, in short, how the present flora has issued little 
by little from the tropical Eocene flora—how, by degrees, the forms 
of warm climates, then those of temperate ones were added to the 
tropical forms, which retired before them in the same proportion, 
leaving their rivals to constitute alone the modern vegetation. 
We see also that in the beginning it is the Indo-Australian types 
that compose the flora; but as the element which is gradually 
added has a very decided American complexion, the vegetation 
assumes, in proportion as it is augmented, a more and more 
American character, which afterwards wears off, and at the diluvial 
period again, to a great extent, disappears. 

All these researches, both upon the fossil plants and animals, 
coincide in obliging us to regard the climate of Europe generally 
as warmer during the Tertiary period than at the present time— 
as subtropical, similar to that of the southern United States, and 
specially Louisiana. But in a given locality there were differences 


according to the periods, and at a given period differences accord- . 


ing to the localities. Thus, at the Upper-Eocene period, the mean 
temperature in any part of Europe was probably 13 or 14 degrees 
higher than it is now in the same locality; at the period of the 
Lower Miocene the difference was only 9 degrees, during the 
Upper Miocene 7; and in the Pliocene period it fell to 3 degrees. 
And thus, again, at any one period the climate was fa> from being 
the same in the different parts of Europe: there was a distribution 
of the heat according to certain zones; and all the researches, 
especially the study of the fossil plants of Iceland (which is par- 
ticularly instructive in this respect), agree in demonstrating that 
that distribution took place in precisely the same manner as at the 
present day.—Annales de Chimie et de Physique, October 1878, 
t. xv. pp. 157-161. 


ON THE DIFFUSION OF LIQUIDS. BY J. STEFAN. 


In this memoir the observations made by H. Voit and Hoppe- 
Seyler on the diffusion of sugar-solutions, by the saccharimetric 
method, are first discussed, and compared with the theory of dif- 
fusion advanced by Fick. Of these experiments those instituted 
by Hoppe-Seyler on the diffusion of urine-sugar accord best with 
the theory; and from them the coefficient of diffusion can also be 
determined, which is found =0-42, taking the centimetre as the 
unit of length, and 24 hours as the unit of time. 

Hoppe-Seyler’s observations, made with another saccharimeter, 


Intelligence and Miscellaneous Articles. 75 


on the diffusion of cane-sugar, as well as the analogous experiments 
of Voit, show such wide deviations from the theory that the cal- 
culation of them according to the formule derived from it has no 
meaning. 

Further, the experiments instituted by Johannisjanz, after the 
prism method described by Kundt, are considered, of which the 
formal differences from the theory do not appear to be great; yet 
the coefficient of diffusion of common salt through water, calcu- 
lated from them,.namely 0°45, is too little by more than half. 
From the determinations made by Fick upon the same salt, the 
values 0°94 for 15° and 1:13 for 20° temperature are deduced for 
this coefficient ; and these values agree with Graham’s experiments, 
as well as with some to be subsequently published. 

The great errors by which the results obtained by optical methods 
are affected proceed from the fact that the hypothesis on which 
those methods are based, viz. that a horizontal beam of light which 
falls upon a vertical plane bounding a diffusing liquid remains 
horizontal during its passage through the liquid, is incorrect. 
Such a liquid, bounded by two parallel sides whose density dimi- 
nishes from below upwards, behaves like a prism whose refracting 
edge is directed upwards; or, inasmuch as the diminution of 
density of the liquid is not uniform from below upwards, it ex- 
hibits, together with the properties of a prism, also those of a 
cylindrical lens. Several experiments are described in the memoir 
by which these peculiarities of solution are proved. 

The author, in conclusion, refers to the analogous behaviour of 
sound when it is propagated in or against the direction of a wind 
the velocity of which increases upwards, from which behaviour 
Stokes first explained the fact that in the former case a sound is 
heard at very great, in the latter at only very short distances.— 
Kuiserliche Akademie der Wissenschaften in Wien, mathem.-naturw, 
Classe, Dec. 5, 1878. 

ON THE SPECIFIC HEATS AND HEAT OF FUSION OF GALLIUM. 

BY M. BERTHELOT. 

1. M. Lecog de Boisbaudran having had the kindness to place at 
my disposal an ingot of gallium weighing 34 grams, I have deter- 
mined its specific heat in both the liquid and the solid state, and its 
heat of fusion. J worked according to my usual methods and with 
the aid of my water calorimeter. IJtis known that gallium fuses at 
+30°, but may be kept liquid, in the state of superfusion, down to 
near Zero. 

2. Two trials, one made between 119° and 18°, the other between 
106° and 12°-5, gave 0:0802 as the value of the specific heat of 
hquid gallium. 

3. The specific heat of solid gallium, between 23° and 12°, was 
found to be equal to 0-079. 

This quantity must not be measured too near the melting-point. 
Two trials made between 28° and 13°, great care being taken not 
to heat the metal above 28°, in order not to melt it, gave the ab- 
normal values 0-275 and 0°352; but I perceived, at the same time, 


76 Intelligence and Miscellaneous Articles. 


that the fragments of the metal were. soldered together at places, 
under the influence of a partial softening: these numbers therefore 
include a portion of the heat of fusion. 

_ 4. The heat of fusion of gallium can be easily determined. By 
introducing some crystals into the superfused gallium, the whole 
of the metal crystallizes rapidly. At 13° I thus found +19-14 
and +19:°08, mean +19-11, for the unit of weight. 

This number remains sensibly the same for every temperature 
between 30° and zero, on account of the specific heats of the liquid 
and the solid being nearly identical. Referred to the atomic weight, 
it becomes 1°33 calory. 

5. It will be observed that the two specific heats of gallium, taken 
near the same temperature, are nearlyidentical. Mercury presents 
the same peculiarity, its specific heat bemg, according to Regnault :— 


0-0319 between —40° and — 78°; 
0:0333 between zero and 100°. 


It is the same with the other metals. Thus the specific heat of 
melted lead between 350° and 400°, according to Person 0-040, 
exceeds by only one fifth that of the same metal, solid, at the ordi- 
nary temperature, or 0-032. 

The same with tin (0°056 cold, 0-063 at about 300°). 

The same with bismuth (9:031 cold, 0°036 at about 320°) :— 
slight deviations, attributable in great measure to the difference of 
the temperatures, as the specific heats go on increasing with the 
temperature. It may be assumed that the solid and liquid specific 
heats of all these metals, if taken at the same temperature, would 
have values very near one another. 

6. The atomic weight of gallium, recently determined by M. 
Lecog de Boisbaudran, being 69:9, its specific heat in the liquid state 
is equal to 5:59, in the solid state to 5°52. 

This product is the same for aluminium, or 5°53 (Kopp), and 
for glucinium, according to MM. Nillson and Pettersson’s new 
measurement, or 5°64, 

With these may be compared the analogous metals, such as zine, 
6-08 (Kopp), and magnesium, 5°88 (Kopp) 

Manganese (6°69), so similar to the last metals, and crystallized 
silicium (4°62), of which the oxide and chloride, on the contrary, 
remind us of aluminium, give products which deviate much, and in 
opposite directions, although by quantities nearly equal, when 
compared with the atomic specific heat of aluminium: the total 
deviation here amounts to nearly 50 per cent. 

I shall not here repeat what I have had occasion to say in this re- 
spect relative to the limits of theoretic and practical uncertainty of the 
law of Dulong and Petit in its applications to solid elements (see 
Comptes Rendus, t. Ixxxiv. pp. 1261-1276). In reality that law 
only presents a precise and incontestable meaning for the simple 
gases, the only bodies for which it is permissible to assume that one 
and the same rise of temperature answers to one and the same in- 
crease of vis viva under the same volume.—Annales de Chimie et de 


Physique, October 1878, t. xy. pp. 242-244. 


sin ab dar a tale aaa 


THE 


LONDON, EDINBURGH, ax» DUBLIN 
PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES.] 


meets ly U AR Y 1s79. 


XI. Investigations on the Nature of Spectra (1. Theory ; 
2. Spectra of Mixed Gases). By HitHarp WIEDEMANN™. 


ale the path-opening investigations of Bunsen and 
Kirchhoff the spectra of incandescent gases have been 
subjected to a more searching elaboration ; and it has been re- 
peatedly endeavoured to ascertain theoretically the reasons for 
the occurrence of line and band spectra, to discover relations 
between the individual lines which compose them, as well as 
to explain the variations which they undergo through pressure 
and change of temperature. 
As, however, the physicists in question mostly enter more 


closely only into particular points, and but cursorily touch 


upon the causes for the spectral lines without bringing them 
into connexion with other data resulting from the mechanical 
theory of gases, I have tried, partly in continuation of their 
considerations, to form for myself a theory of spectral pheno- 
mena, which should be useful in enabling me to get, first of 
all, fixed points for a series of experimental investigations, the 
first part of which I take leave to communicate supplementary 
to the above theory. 


THEORY. | 
According to the kinetic theory of gases, the individual mo- 


- lecules contained in them move rapidly in all directions. As 


Stefan and Van der Waals have inferred from the experiments 
of Joule and Thomson, between these molecules attractive 


* Translated from a separate impression, communicated by the Author, 
from Wiedemann’s Annalen, vol. v. pp. 500-524. 


Phil. Mag. S. 5. Vol. % No. 41. Feb. 1879: H 


78 M. HE. Wiedemann’s Investigations on 


forces exist to distances which are great in comparison with 
the dimensions of the molecules themselves. At very minute 
distances, however, the molecules must repel one another, 
since otherwise there would be no reason for the recoil of the 
particles after each collision. These repulsions probably pro- 
ceed from the envelopes of ether surrounding the molecules 
of the bodies, and must diminish more rapidly with increase 
of distance than the attractive forces. The rotation and oscil- 
lation of the individual atoms in the molecule about a common 
centre of gravity; which take place in addition to the transla- 
tory motions, lead, at a sufficiently elevated temperature, to 
the division of the molecules into theiratoms. These rotatory 
and oscillatory motions are periodic, and must also call forth 
periodic vibrations in the surrounding luminiferous zther. 

Line Spectra.—Let a rarefied gas be heated to the highest 
possible temperature ; we can then assume that the individual 
molecules are decomposed into their atoms. On the collision 
of these, oscillatory. motions only will occur, since, according 
to the experiments of Kundt and Warburg on the specific heat 
of mercury vapour, as well as the theoretic reflections of Max- 
well, Watson, and Boltzmann, in monatomic molecules the vis 
viva of the motions of rotation is nil. The spectra which 
make their appearance with these elevated temperatures con- 
sist of separate bright lines, the cause of which we have 
accordingly to seek in the oscillatory motion of the atoms, 
since they also occur with the vapours of mercury and cad- 
mium, which are regarded as monatomic. 

Let the gas be so much rarefied that the time which elapses 
between two collisions is very great in comparison with that 
during which the particles are within their reciprocal spheres 
of action ; then, with the motions of the individual ether par- 
ticles, at first with small amplitudes, a limited number of rays 
will be emitted of a different vibration-period, whose wave- 
lengths will depend on the special arrangement of the eether 
among the atoms. If the elongations become greater, say by 
our raising the temperature of the gas, and with it the vis viva 
of each of the colliding atoms, then to these fundamental vi- 
brations certain harmonic ones will be added, the vibration- 
period of which, again, will depend on the arrangement of the 
ether and the forces in action between it and the material 
atoms. 

That many of the individual lines in the observed spectra 
may be regarded as really harmonics of a fundamental vibra- 
tion, Lecoq de Boisbaudran, Stoney, Soret, and others have 
proved by careful calculations. Above all must the intensity 


F Amn 


the Nature of Spectra. 79 


of the higher harmonic vibrations, to which the more-refran- 
gible rays correspond, increase with the augmentation of the 
amplitude; and in fact Lecoq de Boisbaudran finds that, in 
the nitrogen-spectrum, at a higher temperature the blue lines, 
corresponding to the double octave of certain vibrations, come 
out, at a lower the red and yellow, as a fifth of the same vibra- 
tions. Similarly, lithium chloride in the flame of the Bunsen 
burner shows a very bright red and a very faint orange line ; 
before the blowpipe the latter increases in brightness much 
more than the former, though without becoming equal to it ; 
if, however, the induction-spark strikes upon a solution of 
lithium chloride, the orange line is much brighter than the 
red, and the blue lithium-line becomes very bright. Many 
other instances might be mentioned. 

By mere elevation of temperature, also, as F'. Lippich and 
afterwards Pfaundler have argued on theoretical grounds, a 
widening of the lines may also be produced by the molecules 
of the gas having each a high velocity, partly directed towards 
the observer, partly away from him. In far higher measure, 
however, do such widenings of the lines take place when we 
increase the pressure of the gas; the individual vibrating 
zether envelopes of an atom can then only for a brief period 
carry on their motions undisturbed, since they are mostly 
within the compass of the sphere of action* of the other atoms. 
This conclusion is confirmed by the experiments of Wiillner, 
G. Camician, and others. 

Interferences accompanying great Differences of Progress.— 
The time during which an optic motion of the ether of the 
individual backward-and-forward-rushing molecules and atoms 
takes place undisturbed I have endeavoured to ascertain by the 
following considerations :— 

If two rays of light are to interfere, they must start from 
the same point; and during the time which elapses between 
the instants when the first and the second ray are emitted no 


* The diameter of this action-sphere is the length to which, reckoned 
from the centre of the atom or molecule, the zether possesses a state dif- 
fering from that which it possesses in free space; as the temperature rises 
the length will increase at those molecules which are composed of a plu- 
rality of atoms. On the other hand, the so-called molecular diameter 
denotes, in the kinetic theory of gases, the distance up to which the centres 
oftwo molecules can approach each other when they strike one another— 
a distance which essentially varies with the force of the collision, and 
hence may diminish with rise of temperature, as the experiments on the 
friction of gases show. The diameter of the sphere of action will in every 
case be greater than this molecular diameter, since the particles pushing 
against one another must first pass through a portion of the action-sphere 
before their motion reverses its direction. 


H 2 


80 | M. E. Wiedemann’s Investigations on 


disturbance of the vibratory motion can occur in the place in 
question ; at other times sudden changes of phase appear, by 
which the vibrations are altered in a quite indeterminate 
manner. Hence that difference of phases up to which inter- 
ferences are still observable gives a measure for the time 
during which a regular motion takes place at the luminous 
point. The source of light is formed of the great number of 
atoms or molecules which lie in the vicinity of that point. 
Their internal vibratory motion will in every case remain un- 
disturbed only so long as they do not come into one another’s 
sphere of action—that is, during the time, nearly, that elapses 
between two collisions. But this period, for the different mo- 
lecules of the same gas, lies between nil and infinity. A 
preponderating number of them will within a certain very 
short time experience no collisions. Therefore the rays emitted 
at the beginning and end of this period from all these particles 
may interfere, and only those issuing from the few others 
illumine regularly the field of vision in the apparatus used. 
Hence the interferences are sharp. But the longer the time 
which elapses between the emission of the two interfering 
rays, and the higher the interference-bands we observe, the 
fewer molecules contribute to bring them about, the more mo- 
lecules illumine the field of vision regularly, and the less sharp 
do the bands become. Lastly, with phase-differences corre- 
sponding to intervals of time greater than that which is ne- 
cessary for passing through the mean path-length, they will 
very quickly disappear, since most of the molecules collide 
within this period and thus undergo irregular changes of 
hase. 
; There are measurements by Fizeau and Foucault, and more 
recently by J. J. Miller, respecting the higher interferences. 
With sodium-light, interferences corresponding to a difference 
of path of more than 50,000 wave-lengths were not to be seen ; 
with hydrogen those of 20,000 were distinctly visible, and the © 
highest possible phase-difference was not yet reached. 'There- 
fore, with sodium the vibrations must remain regular up to 
50,000 double vibrations at the most—that is (since the sodium- 
line corresponds to about 500 billion vibrations in a second), 
during the time 
_ 90000 
500:10" 


or during a 10000-millionth of a second. We find the timer 
between two collisions, if we divide the mean length of path 
of the gas in question by the mean velocity. ! 

If (since we can only have to do with the order of magni- 


=10-?° second, 


the Nature of Spectra. | ee 


tude of the individual numbers) we lay down for a base 
the mean length of path of the hydrogen molecule at 0° 
(L=194.10-7 centim.) and the mean velocity of the same 
at the same temperature (c=1698 . 10? centim.), we get 


lee tO? 
+ G4 abled 107 


The two quantities T and ragree relatively so well with one 
another that at all events the assumption is not inadmissible 
that the ether particles on the sodium atom may accomplish 
undisturbed, on the average, as many as 50,000 vibrations. 
This investigation shows, at the same time, that we need not 


= 1:14 x 10-" second. 


‘in all cases conceive of the vanishing of interferences. as pro- 


ceeding from a widening of the lines of the spectrum. 

The measuring of the high interferences must also furnish 
us with a means of determining the amplitude of the exther- 
vibrations, and therewith the density of the wether. If the 
length of path in which a particle undergoes no disturbance 
be, say, # millimetres, if the number of the vibrations executed 
upon this path be m, then the motion is disturbed just at the 
commencement of the mth vibration ; the m vibrations, for 
which there is no reason that they should all be perpen- 
dicular to the progressive motion of the molecules, are dis- 
tributed equally over x millims.; the mean magnitude of the 


amplitude in that direction amounts to = millim. 


The distance upon which the molecules undergo no disturb- 
ance it must be possible to determine by heating the gas under 
different pressures to the same temperature, and determining 
the number of the interferences. ‘The length of the molecular 
diameter, S, is independent of the pressure. But if at the 
density 1 the mean distances of the molecules are A millim., 


they are = millim. at the density $; the numbers g and q,, 


however, of the resulting undisturbed vibrations are deter- 
mined by 
A 
A—S ua 
Pegs oo rae 


if T denotes the duration of a vibration, and V the velocity of 
translation of the molecules. Hence, if g and g, be known, 
A and 8 follow immediately. 

‘The available data are nevertheless not yet sufficient for 
carrying out these calculations, the principle only of which is 


82 M. E. Wiedemann’s Investigations on 


here intimated, though I hope soon to be able to communicate 
experimental data for the solution of the above-mentioned 
problem. | 

If we compare the line spectra of chemically similar ele- 
ments, such as potassium, sodium, calcium, and rubidium, 
they show (as was first remarked by Lecoq de Boisbaudran) 
the same groups of lines, only in different places in the spec- 
trum. Hence they are composed of the same harmonic vibra- 
tions of different fundamentals; therefore the configurations 
of the envelopes enclosing the material atoms, or the forces 
acting upon these, must be similar. A displacement of the 
lines corresponding to one another in the spectra in question 
from the red towards the violet signifies, cwteris paribus, an 
increase of the attractive force of the atoms upon the ether 
envelopes enclosing them. 

Band Spectra.—lf we consider gases which are composed 
not of single atoms but of molecules, we shall then often have 
to investigate not the spectra of emission, but of absorption, 
since at the temperatures at which those gases begin to be 
luminous their molecules are already broken up. Whether 
the molecules be composed of homogeneous or heterogeneous 
atoms, the spectra will always be conditioned by the rotatory 
or oscillatory motions either of the entire molecules or of the 
atoms in them or the ether envelopes enclosing the latter ; 
hence they will possess a corresponding character. Thus, 
with simple gases at low temperatures the so-called band 
spectra appear, quite analogously to which the spectra of com- 
binations are composed. Both consist of broad bands of light, 
which upon closer examination prove to be formed of bright 
and dark lines. So it is with nitrogen, and with carbonic 
acid ; just so, as I have repeatedly convinced myself, do the 
haloid compounds of the metals of the alkaline earths, and 
similarly also those of mercury (conf. the experiments of Mr. 
Pierce ina memoir that will shortly appear). 

We will inquire first whether these spectra are to be attri- 
buted to the rotatory motions of the entire molecules*. 

The fundamental vibration of the rotatory motion we can 
calculate approximately by means of the mechanical theory of 
gases. Let m be the mass of a molecule, wu the velocity of 


* A similar view was conjecturally expressed by Helmholtz in a paper 
by J. Moser. Lockyer likewise refers the different spectra of the same 
body to differently complicated complexes of atoms. The question 
whether to the same elements only one (a line spectrum) or a plurality 
of spectra (of lines and bands) can belong, can be decided in favour of 
the latter view by Wullner’s last experiments, as well as by Lockyev’s 
investigations on the absorption-spectra of differently heated vapours. 


the Nature of Spectra. i 83 


translation, v that of rotation, then (neglecting the oscillatory 
motion ) 

1 2 

3g MU Lo 

imu 


a can be calculated from the ratio of the specific heat at con- 

stant pressure and volume, and, for the permanent gases, is 

0°66 nearly; so that the velocity of the rotatory motion, 
v=urv 0°66=u x 0°813. 

Further, let the radius of the molecule be , the number of 
rotations executed in unit time z, while v is the velocity cor- 
responding to the square of the mean velocity of the particles 
contained in the molecule. Ifthe entire mass of the molecule 
were situated at the extremity of the molecular diameter 27, 
then would v be the periphery-velocity, and the number of the 
rotations in unit time 


Disa toon! ts OS ES) 

Ona lar 
As, however, this is not the case, but there are also mass-par- 
ticles nearer to the centre, the real periphery-velocity must be 
greater than the mean value v (and the number of rotations, 
z, therefore greater), yet always of the same order as the value 
which results from the above formula. An exact determina- 
tion could only be obtained if the shape of the molecules were 
perfectly known. 

For ordinary temperatures, with hydrogen u=1698 metres, 
with nitrogen 453 metres ; 7 with the same two gases, accord- 
ing to Riihlmann’s calculation of Regnault’s experiments in 
the way indicated by Van der Waals, = 20 x 10—!! metre and 
Pe) metre. 

For hydrogen we have thus, very nearly, 

“=11x 10", therefore a billion ; 


for nitrogen, about 


| 3°4 x 10". 

To every rotation of the at all events not spherical molecules 
corresponds a displacement of the ether, or a fundamental vi- 
bration. Mostly, however, it does not lie within the region 
of the visible rays; but probably we can observe certain har- 
monic vibrations, perhaps those which follow one another with 
from 500 to 1000 times the velocity. That in fact, on the 
occurrence of band spectra, harmonic vibrations to over the 
700th are visible has been proved by the calculations of Stoney 
and Reynolds for the spectrum of chromium oxychloride ; they 
have also shown that, with a suitable choice of the constants, 
rhythmic arrangements in the degrees of brightness of the 


84 M. E. Wiedemann’s Investigations on 


different lines can be recognized as characterizing the band 
spectra. 


The assumption, however, that the band spectra are gene- | 


rated by rotatory motions*, is opposed by the consideration 
that, if when the temperature is raised the light emitted by 
gases always consists of rays of the same wave-length, the 
molecular diameter must increase proportionally to the abso- 
lute velocity, or to the root of the absolute temperature, since 
only then could the number of rotations remain invariable. In 
all other cases the lines must be displaced towards the red or 
the violet, according as the molecular diameter increases. with 
rising temperature more or less quickly than the velocity of 
rotation. Thatsuch displacements do not occur we learn from 
all the spectrum-experiments hitherto made. 

Experiments, subsequently to be communicated more fully, 
have shown me how wide are the limits within which the bands 
retain their situation. In those experiments nitrogen was 
heated by the induction-spark to 4000° and 20000° respectively, 
and yet there were no alterations of position in the band spec- 
trum. The temperatures were determined calorimetrically. 
It is therefore in the highest degree improbable that the above 
spectra ought to be ascribed to the rotations of the molecules. 
Perhaps the frequently occurring augmentation of brightness 
of the background from which the spectral lines stand out may 
be referred to them. 

Spectra of Compounds.—In order, therefore, to explain the 
band spectra of the elements, and the spectra (composed quite 
analogously to them) of chemical compounds, we assume that 
they are produced by the vibrations of the atoms in the mole- 
cule or of their ether envelopes. That, at the same time, the 
spectra of the compounds are so much more complicated than 
the (line) spectra of the free atoms can cause us no surprise. 


If we further compare the spectra of the undecomposed. 


compounds with the band spectra possessed by the elements 
which compose them, we find that the position and grouping 
of the lines, as was to be expected, are essentially ditferent in 
the former from what they are in the latter; for indeed the 


* Lecogq, indeed, is inclined to account for both band and line spectra 
by rotations of the molecules about centres not precisely determined, the 
motion following elliptical paths, these centres again rotating about other 
centres, and so forth. By admitting several such centres, and by a more 
precise determination wether the motion in the various ellipses takes 
place in the same or in opposite directions, he succeeds in explaining the 
various observed phenomena; but he gives no physical reason, deduced 
from other well-known phenomena, for the assumption of that sort of ro- 
‘fatory motions. : 


a eee 


| 


the Nature of Spectra. 85 


forces conditioning in these the vibrations of the xther are 


of an intrinsically different nature from those in the mole- 


cules built up out of the atoms of the same elements; but when 
the grouping of the atoms in the compounds and in the mo- 


lecules of the elements composing them are similar, the general 
appearance of the spectra given by both will also be the same, 
even if the individual lines in them do not coincide. Thus it 
is with the absorption-spectra of iodine vapour, vapour of bro- 
mine, and the vapour of monochloride of iodine closely in- 
vestigated by Roscoe and Thorpe. In like manner must com- 
pounds of analogous composition also furnish similar spectra 
—as, for example, the haloid compounds of the earth-metals, 
mercury, Xe. 

If we can succeed in determining for the band spectra of 
the elements or compounds the fundamental vibrations, and if 
the motions are conditioned by the forces in action between 
the atoms, we must be able to determine these in absolute and 
relative measure from the absolute weight and mutual distances 
of the atoms, which are at any rate determinable by the newer 
theory of gases. Intimations for such investigations we find 
in the displacements which, according to Mitscherlich’s, Lecoq 
de Boisbaudran’s, and others’ observations, certain groups of 
lines undergo on the transition from a chlorine to a bromine 
or an iodine compound. From the thermal processes alone 
which accompany the formation and decomposition of the com- 
pounds this is indeed not possible, because, even when we let 
the elements act upon one another in the gaseous state, the 
quantities of heat that appear are still conditioned by the in- 
determinable separation of the atoms which form the molecules 
of the elements. 

As we ascribe the band spectra to combined, but the line 
spectra to the atoms isolated at higher temperatures, it can be 
alleged that ceteris paribus the former more readily occur 
with bodies which are with more difficulty subject to che- 


-mical actions, and therefore to decompositions, than with less- 


stable bodies. G. Wiedemann has pointed out that by an elec- 
tric discharge which corresponds to the compensation of equal 
differences of potential, equal amounts of heat are generated 
when it passes through different gases which are present in 
the same capillary tube and under equal pressure. If these 
gases (for example, hydrogen and nitrogen) possess equal 
specific heat even at the temperatures to which they are heated 
by the discharges, and disintegration does not occur, the tem- 
peratures attained must also be equal. Nevertheless nitrogen, 
which is chemically more stable, shows the band. spectrum, 
hydrogen the line spectrum. Chlorine, bromine, and iodine, 


86 M, E. Wiedemann’s Investigations on 


whose great capacity of reaction indicates that their molecules 
are easily broken up, almost constantly show line spectra. That 
different substances at the same temperature possess different 
kinds of spectra we might also be inclined to infer from the 
fact that in the same Geissler tube, which contains at the 
same time hydrogen and nitrogen, the nitrogen bands appear 
together with the hydrogen-lines. This inference, however, 


is not absolutely correct, since, as we shall subsequently see, - 


in a mixture of gases the passage of electricity is brought 
about with different degrees of facility by the molecules of 
different substances. 

In complete accordance with this are the results obtained 
by M. Wiillner, who found, when he caused discharges to pass 
through gases at a determined pressure, that now line and 
now band spectra appeared, according as the equalization of 
the electricities ensued as a tuft or a spark. The latter ex- 
tended to only a few, the former to great number of particles. 
As in general at each discharge of a definite collecting-appa- 
ratus with an equal charge an equal quantity of electricity 
passes, the temperature in the spark must be much higher 
than in the tuft; hence in the spark discharge a breaking-up 
of the molecules into their parts is much more probable than 
in the tuft discharge*. Moreover the behaviour of mercury 
vapour proves that a band spectrum is not constantly com- 
bined with the tuft discharge, nor a line spectrum with the 
spark discharge. If mercury is introduced into wide tubes, 
and heated, and the discharge of the induction-coil passed 
through, the luminous particles of mercury fill the entire tube ; 
and yet it shows only the line spectrum. Sodium behaves 1 in 
just the same manner. 

Disagreeing with the views we have now unfolded, some 
have supposed that the differences between band and line 
spectra could be explained by mere alterations of pressure or 
equivalent alterations in the thickness of the luminous layer 
of gas. This idea, however, is hardly tenable in the face of 
Lockyer’s experiments, who introduced into a glass tube, 5 
feet in length, through which a slow current of hydrogen was 
passing, a small piece of sodium, heated the entire tube to red- 
ness, and let the light of an electric lamp pass through its 
length, which he then examined with a spectroscope. The 


* To decide the question why in certain gases which principally give 
line spectra (as chlorine, bromine, iodine) spark discharges are much more 
readily formed than tuft discharges, further experiments are still required. 
Probably a much higher potential is necessary for the discharge in them 
than in the other gases, to which, perhaps, the shortness of the path-length 
of chlorine points. 


se 4 


the Nature of Spectra. ; 87 


double line of sodium appeared dark, but not thicker than in 
a short tube under the same conditions, and much thinner 
than when the density of the sodium was only a little increased. 
What was here proved for sodium vapour may in an analo- 

ous manner hold good for the other gases, such as nitro- 
gen &. Atall events the above experiment shows that changes 
of thickness must not be supposed to run parallel with changes 
of density. In order that this should be the case, the curve 
which represents the dependence of the coefficient of absorp- 
tion would have to be perfectly identical with that which ren- 
ders the disturbance (conditioned by the greater number of 
the collisions in consequence of the greater density) of the 
vibrations of the ether envelopes as a function of the number 
of the collisions (which is extremely improbable), while the 
widening of the lines would be fixed by the former curve at 
increasing thickness, by the latter at increasing density of the 
absorbing layer. 

Further experiments, by Lockyer, Schuster, and others, 
teach besides that sodium, as well as the vapours of other 
metals, possess different absorption-spectra at different tempe- 
ratures, yet without the limits within which the thickness of 
the absorbing stratum varies being very wide. From this 
may also be explained the recent experiments of Liveing and 
Dewar, who vaporized sodium in a vertical tube heated below 
to a white heat, the bottom of which served at the same time 
as the source of light; they then introduced from above to 
various depths a tube containing hydrogen, and observed the 
changes of the spectrum. Thereby, on the one hand, the 
thickness of the layer through which the rays passed was 
varied, but, on the other, when the tube was sunk deeper the 
most extremely absorbent layers had certainly a much higher 
temperature than when it was lowered to a less depth”. 

Spectra of Solids and Liquids.—If we condense gases into 
the solid or liquid state, the vibrations in the individual mole- 


* It might at first appear as if the action of the molecules in a body 
upon a luminous ray which passes through it (as exemplified in disper- 
sion, absorption, the rotation of the plane of polarization) were not pro- 
portional to the number of the acting molecules in the unit of volume (as, 
we learn from experiment, it is), but to the number in the unit of length, 
and therefore to the third root of the former. Butifwe employ a method 
analogous to that which serves for ascertaining the number of the collisions 
of a molecule in a space filled with other molecules of gas, we see that 
the vibrations of the luminiferous ether are affected by all the molecules 
which are present in a cylindrical space whose radius is equal to the 
radius of action of a molecule upon an ether particle. But the number 
of molecules in such a space increases proportionally to the total number 
of the molecules. 


88 M. BE. Wiedemann’s Investigations on 


cules almost never continue undisturbed; in the absorption- 
spectra (to the examination of which we are here almost ex- 
clusively directed), sharp absorption-streaks appear only in 
isolated cases—with the salts of uranium, didymium, and sub- 
stances of analogous composition to potassio-chromic oxa- 
late. The last-mentioned shows in its absorption-spectrum, 
beside a broad band in the orange and yellow, a sharp black 
line in the red. The absorption of single rays or groups of 
rays corresponds to the vibrations of the atoms composing the 
molecules or their proximate constituents. Hence, ifa group of 
atoms occurs in different combinations, it calls forth in general 
the absorption-spectrum corresponding to it (nitrocompounds, 
chromates), which, however, may be more or less modified by 
the presence of other atoms with those occurring in the mole- 
cules. Thus all the salts of didymium show on the whole the 
same absorption-spectra; but the individual lines are some- 
what displaced, sometimes towards the violet, sometimes 
towards the red, according to the nature of the acid. Upon 
the atoms of the absorbent part of the didymium group the 
acid evidently exerts an attraction which does not extend 
equally to all of them, and therefore does not produce a mere 
shifting of the centre of gravity of the system. Then, accord- 
ing to the position of the acid and the strength of its attrac- 
tion, the vibration-period may be increased or lessened. 

Nevertheless this is not always the case. Thus experiments 
made at my suggestion by M. Pierce, with the chromic oxa- 
lates of potassium, sodium, lithium, and silver, showed that 
the sharp streak in the red, quite independently of the nature 
of the shifting constituent, the metal, always retains the same 
position, even when the solution is heated. We must there- 
fore admit that the action of these metals upon the absorbing 
group of atoms is unperceivable. 

Pleochroism.—In a similar way may pleochroism be ex- 
plained. The vibrations which take place in the molecules 
that build themselves together in a definite manner to form 
crystals are affected very differently by the neighbouring mo- 
lecules, according as they take place in one or the other direc- 
tion; or else, in molecules thus arranged, the motions in dif- 
ferent directions have from the beginning different fundamental 
vibrations. To derive pleochroism at once from differences in 
the dispersion of the different rays is surely not admissible, 
since the different dispersion is, according to the newer theo- 
ries, just a consequence of difference in the strength of the 
absorption; on the contrary, a connexion between the two 
quantities is certainly to be expected. 


the Nature of Spectra. — 89 


Displacement of the Spectra in Solutions.—I am inclined to 
attribute, at least in part, to chemical influences those dis- 
placements which the absorption-streaks of various materials 
undergo according to the substance in which they are dis- 
solvyed—especially in the case of organic colouring matters, 
the quickly commencing decomposition of which in solutions 
indicates the chemical influence of the solvents. The influ- 
ence of the dispersion of the solvent may be checked, since 
solutions, for instance, of potassio-chromic oxalate in water 
and in glycerine show the absorption-streak in exactly the 
same place in the spectrum, although the dispersions of these 
two substances are sensibly different. 

The question, finally, which has lately been repeatedly dis- 
cussed, of the difference of the spectra, both of emission and 
absorption, of one and the same substance under different 
conditions (H. W. Vogel and J. Moser), it appears to me may 
be solved thus (provided the above considerations are true):— 
Within the molecules of any chemical compound, which are’ 
withdrawn from the influence of the molecules in their vici- 
nity, perfectly definite vibrations take place, conditioning 
completely determined spectra; butas soon as these molecules 
come nearer to one another, or, in liquids or solids, form more 
complex (multiple) molecules, or, finally, in solutions are in- 
fluenced also by the action of another substance, the spectra 
may change their appearance. That two different substances 
give perfectly identical spectra is thinkable only when the 
forces acting between the atoms in their molecules are iden- 
tical. 

It is my intention to test by experiments, and pursue fur- 
ther, the views which have now been unfolded, and which very 
well explain a great number of the facts that have hitherto 
been observed. But for this, it is before all things necessary 
to examine the spectra under completely determined condi- 
tions of temperature and pressure. 

The most convenient means for the production of elevated 
temperatures, such as are necessary to call forth gas-spectra, 
is, decidedly, the electric spark. Hence the temperatures 
generated by it must be exactly ascertained; and, above all, 
we must accurately settle whether it calls forth the luminous 
phenomena by elevation of temperature alone. 

In order first to decide the last point, I tried whether, in 
mixtures of two gases through which a discharge passes, the 
spectra of both substances constantly make their appearance, 
or only one of them. 


90 M. H. Wiedemann’s Investigations on 


SPEcTRA OF MIxED GASES. 


Disharges in Mixtures of the Vapours of Mercury and Sodium 
with other Gases. 


Ina Geissler tube filled with hydrogen a little mercury was 
hermetically enclosed and the tube heated in an air-bath, 
while at the same time the current of an induction-apparatus 
passed through it. Whilst at the ordinary temperature the 
hydrogen-spectrum was obtained, with the heating the lines 
of mercury were added; these became brighter and brighter 
as the temperature rose; and at the same time the hydrogen- 
lines disappeared both in the wider portions of the tube and at 
the electrodes *. 

In order to accurately investigate and with certainty estab- 
lish this phenomenon multifarious experiments were made. 
The tubes employed were either of the usual form of a Geissler, 
consisting of a central capillary part and two wider parts at 
the extremities, or they were prepared from a wide tube by 
drawing out and thus narrowing the middle portion before 
the blowpipe-flame, or else they consisted of a tube of uniform 
width (about 10 millims. diameter) and 50 millims. length. 
Finally, the shape of the electrodes (constantly of platinum) 
was varied: either they were both spherical (diameter 3 
millims.), or one spherical and the other pointed, or both 
pointed. 

For the filling and exhaustion of the tubes, two side pieces 
were joined on by fusing, of which the one was hermetically 
closed, at about 1 centim. from the wall of the tube, immediately 
after drying, while the other was connected with the air-pump. 
This also, as soon as the intended pressure was generated in 
the tube, was melted off, leaving a length of from 2 to 3 centims. 
If further measurements were to be instituted at a different — 
pressure from that at first employed, the point was broken off, 
the tube exhausted, and again hermetically sealed, and so on. 
With a little care the tube could thus be used successively 
three or four times. - 


* This method of producing the spectrum of mercury may be of value 
in optical investigations in which it is necessary to have homogeneous 
light of a determined wave-length. While in the red the lines of lithium 
and hydrogen (of which the blue-green and violet lines can be easily in- 
tercepted), in the yellow the sodium-line, in the blue-green and violet 
likewise hydrogen-lines are at disposal, homogeneous green light is onl 
to be obtained with difficulty, on account of the great volatility of thal- 
lium. The mercury-spectrum is distinguished by a very beautiful green 
line, from which the other, brighter lines (a double yellow and a violet) 
are sufficiently distant to be covered by a diaphragm or eliminated by 
suitably coloured glasses. 


the Nature of Spectra. 91 


The tubes were then fixed insulated and horizontal in an 
air-bath of iron, 16 centims. deep, 11 centims. wide, and 14 
centims. long, by means of glass tubes which passed through 
the two side walls of the bath. The front and back walls of 
the bath were formed of plates of mica; and another mica 
plate served as a cover. The heating was effected by a gas- 
burner placed beneath. The progress of the phenomena was 
examined both during the heating and especially during the 
cooling. The temperatures were measured by an ordinary 
thermometer placed immediately on the Geissler tube. 

For the examination of the spectra either a Bunsen spec- 
trum-apparatus or a Browning direct-vision spectroscope was 
used. ‘To the former, in the place of the hair cross in the ob- 
servin g-telescope, a slit-diaphragm was applied, in order to 
blind off certain portions of the spectrum. 

A middle-sized Ruhmkorff induction-apparatus served as 
the source of electricity, its primary current being furnished 
by 3 or 4 Bunsen elements; a small induction-apparatus, 
however, or a Holtz electrical machine was also employed. 
Tn all cases the same phenomenon was shown. At a not too 
high temperature (between 100° and 200°) the lines corre- 


sponding to the gas contained besides the mercury in the 


Geissler tube disappeared. At the same time a clear differ- 
ence between the two electrodes was observable. When, on 
slowly heating, at the positive electrode and in the whole of 
the luminous tuft issuing from it mercury-lines alone were 
already to be seen, at the negative hydrogen- and nitrogen- 
lines were still distinctly shown, which at higher temperatures 
(at which larger quantities of mercury were present in the 
gaseous space) likewise vanished. 

The best idea of the progress of the phenomenon will be 
given by the following series of experiments. The tube was 
of uniform width, the electrodes spherical; the large induc- 
tion-apparatus served as the source of electricity. The pres- 
sure of the enclosed air amounted to about 10 millims. The 
tube was first heated to 240°, and then permitted to cool 
slowly. 

Above 240°, everywhere only the mercury-lines are to be 
seen, both in the middle of the tube and at the electrodes. 
The discharge issues as a zigzag line of light from the fore 
end of the positive knob, and plays round the negative, without 
any perceptible dark space between. At the wire to which 
the negative knob was fastened, no light is to be seen. 

Between 230° and 210° the nitrogen-lines, together with 
those of mercury, begin to appear at the negative electrode; 
and at the same time the dark space unfolds itself, the wire of 


92 _ M. BE. Wiedemann’s Investigations on 


the negative electrode becomes bright, and the positive dis- 


charge spreads out into a luminous tuft. At 160° the green 
nitrogen-lines are distinctly seen, and the lines of mercury 
become more feebly luminous. At 130° the mercury-lines 
at the negative electrode are less bright than in the positive 
luminous sphere. First at 100° do traces of the nitrogen- 
lines appear in the luminous tuft and at the positive pole, and 
come out more and more with a further lowering of the tem- 
perature. . 

The same phenomena were displayed at pressures of 30, 60, 
and 100 millims.; the nitrogen-lines then made their appear- 
ance in the positive tuft at temperatures between 100° and 


140°. Above 230°, everywhere only mercury-lines could be 


seen. 


In another experiment some mercury was introduced into a 


Geissler tube containing hydrogen. Before the heating, in 
the capillary part the hydrogen-lines showed distinctly. On 
heating, they disappeared, and did not reappear with the cool- 
ing. Hven when the current was interrupted for some time, 
they showed themselves only for a moment after its closing. 
It is probable that, at the first heating and cooling, some traces 
of mercury were precipitated in the capillary tube. The glass 


was then heated so strongly by the passage of the electric 


spark that they were vaporized. Not till the tube was wholly 
immersed in a mixture of ice and salt, and thereby the glass 
made very cold, so that the layer of yellowish mercury (oxide?) 
no longer furnished enough vapour, did the hydrogen-lines 
reappear. 

In order to discover whether other metallic vapours have 
the same properties as are exhibited by mercury vapour, some 
sodium was enclosed with hydrogen or nitrogen. Here also, 
at the heating, the nitrogen- and hydrogen-lines vanish: 
and this commenced earlier at the positive than at the negative 
pole. At temperatures at which the glass began to soften, 
there remained only the yellow, green, and blue double lines 
of sodium visible. That in these experiments the fused sodium 
did not chemically combine with the nitrogen present, and 
that the disappearance of the nitrogen-lines was not conditioned 
thereby, was made known by the fact that, differing from 
Salet’s experiments, the hydrogen- and nitrogen-lines again 
made their appearance after the cooling. 

If a spectrum-tube filled with nitrogen and hydrogen be 
suitably heated at one part far below redness, very slight traces 
of sodium and other metals from the glass are vaporized there; 
and there also the hydrogen- and nitrogen-lines almost com- 
pletely disappear, together with the metallic lines that occur. 


—e se 


the Nature of Spectra. | oe 


Very hot spark discharges even might exert similar actions. 
But we cannot hence infer that the hydrogen itseif vanishes 
or is transformed into a material of another nature. 

The above-described phenomena might result from several 
causes. (1) The vaporized mercury may crowd the other 
gases out of the hotter portions of the tube into the colder, so 
that its own vapour alone is found in the path of the spark. 
(2) The phenomena depend on differences of temperature oc- 
curring in the spark itself when the discharge passes through 
gases mixed with mercury and also through pure gases. 
(3) They are conditioned by this—that whenever any two 
gases are mixed, only one of them becomes luminous. (4) Mer- 
cury particles are torn from the electrodes, and carry over the 
electricity in disruptive discharges. (5) Mercury behaves 
towards electricity essentially otherwise than hydrogen and 
nitrogen. | 

To test the first assumption the Geissler tubes were placed 
vertically instead of horizontally. Ifthis assumption had been 
correct, the behaviour of the upper must then have been essen- 
tially different from that of the under parts—which, however, 
was not thecase. A further argument against this assumption 
is, that in tubes of equal width throughout the phenomena 
were as well exhihited as in tubes with a capillary middle 
piece. 

Secondly, that the disappearance of the lines is not condi- 
tioned by differences of temperature in the spark itself, follows 
from the fact that when the most different sources of electri- 
city are employed (which produce very differently heated dis- 
charges) it equally occurs, that it is also independent of the 
nature of the electrodes, and that it is exhibited in the wide as 
well as in the narrow portions of the Geissler tubes (in which 
the temperatures differ considerably). Further, if we view in 
the rotating mirror the discharges of a Holtz machine that 
take place in a Geissler tube, the intervals between them after 
the heating, when the mercury-lines appear, are not essentially 
other than at the ordinary temperature, provided only that the 
pressure in the Geissler tube has not varied during the expe- 
riment—which it was easy to secure by keeping it constantly 
connected with the air-pump. Since the intervals do not vary, 
equal amounts of electricity pass in equal times, and the tem- 
peratures of the incandescent particles of gas will not be very 
different. 

Thirdly, in order to establish that the appearance of the 
spectrum proper to nitrogen was not prevented by the addi- 
tion to it of any considerable quantity of any gas or vapour 
whatever on the passing of the electric spark, some iodine was 


Phil. Mag. 8.5. Vol. 7. No. 41. Feb. 1879. I 


94 Investigations on the Nature of Spectra. 


enclosed in one of the tubes of average width, with points as 
electrodes ; the pressure of the nitrogen amounted to about 10 
milliims, Hven when it was heated to 220°, the nitrogen- 
spectrum was still distinctly visible together with that of 
iodine—though, it is true, a series of dark absorption-lines 
proceeding from iodine vapour were drawn through it. As 
the iodine vapour filled the whole of the tube, the light (which 
was emitted from the incandescent gas occupying only the 
middle of the tube) must have passed through a.considerable 
thickness of it. At all events the tension of iodine at 220° is 
much greater than that of mercury at the same temperature, 
since the former boils at 180°, but the tensions of the latter are 
uncommonly small (at 100°, according to Regnault, 0-146 
millim., at 140° 3:059, and at 200° 19:19). Nevertheless in 
the mercury-tubes the nitrogen-lines disappeared, even with 
100 millims. pressure of nitrogen, at 140° at the positive elec- 
trode*. : 

Fourthly, that the phenomenon cannot be conditioned by 
mercury precipitated on the electrodes being disruptively car- 
ried away we learn, first, from the experiment described on 
p- 92; and then, again, it was indicated by observations 
which were made with glass tubes without internal electrodes, 
in which the ends were only coated with tinfoil, and yet, when 
the coverings were connected with the sources of electricity, 
the nitrogen-lines vanished nevertheless. 

To mercury, therefore, must be attributed a behaviour 
towards electricity which differs from that of hydrogen and 
nitrogen. We might assume that the mercury molecules 
alone take part in the discharges, or that they take a prepon- 
derating measure of the electrical charge. 

In the mercury vapour mixed with hydrogen the discharge 
perhaps takes place in this way:—There is an accumulation of 
electricity at the electrodes; and this distributes itself to the 
molecules of the surrounding gas. But the mercury mole- 
cules will be more charged than those of hydrogen; and by 
them will the discharge be chiefly brought about, because on 
their encountering other mercury and nitrogen molecules they 
will in preference give up their electricity to the former. But 
the passage of the electricity conditions the luminous pheno- 
mena; hence only mercury-lines appear. 

Since, further, the electrodes do not behave alike, but the 
nitrogen-lines are much longer visible at the negative than at 
the positive electrode, we may perhaps assume that mercury 
charges itself more readily with positive than with negative 


* Even mixtures of hydrogen and nitrogen constantly show the spectra 
of both gases. 


A Method for Adjusting the Collimator of a Spectroscope. 95 


electricity, and therefore exerts a more powerful attraction 
upon the positive than the negative. (On the different be- 
haviours of positive and negative electricities, compare also 
G. Wiedemann and R. Riihlmann.) 

If these experiments show that the passage of electricity 
from one particle to another takes place in various ways in 
different substances, and that, independently of the total tem- 
perature of the mixture, only certain particles are rendered 
luminous by the electric spark, we may further have to take 
into consideration that the passage of electricity from atom to 
atom is capable of producing oscillatory motions of their ether 
envelopes, yet without augmenting in corresponding measure 
the vis viva of the progressive motion of all the particles, as 
would be necessary according to the theory of gases. We find 
an analogy to this in the augmentation of the interior motion 
in a molecule without a corresponding increase of the oscilla- 
tory motion of the whole when non-luminous discharges pass 
through different gases: the latter undergo decompositions 
which otherwise would only be produced by considerable ele- 
vations of temperature. Similarly, in the phenomena of 
fluorescence, by the incident ether-vibrations the vis viva of 
the translatory motions is, for certain vibrations, increased in 
a way that corresponds to a direct augmentation of the pro- 
gressive motion by heating to 500° and more. 

In order to put these assumptions to the proof, I havealready 
commenced a series of experiments, in which the temperatures 
of the discharges in Geissler tubes under various conditions 
are determined. 


Leipzig, August 1878. 


XII. An easy Method for Adjusting the Collimator of a Spec- 
troscope. By ArtHuR ScuusteR, Ph.D., F.R.AS.* 


HE ordinary method for adjusting the collimator of a 
spectroscope for parallel rays is only applicable to the 
mean rays of an achromatic combination. At the extreme 
ends of the spectrum a readjustment has to be made. If the 
ultra-violet rays are observed, and if the lenses are of quartz, 
the ordinary method cannot be used. The followmg method 
is so simple that I cannot help thinking it has often been in 
use ; yet I have nowhere seen it described, and I know that 
others, like myself, have often found a difficulty in making 


* Communicated by the Physical Society. 
[2 


96 Dr. A. Schuster on an easy Method for 


the adjustment without much loss of time and with simple ap- 
paratus. 

The adjustment, as the following consideration will show, 
can be made on each line of the spectrum without any appa- 
ratus whatever. The only requirement is that the prism should 
be movable. 

Suppose the rays which fall on the prism to be either con- 
vergent or divergent; then, after their passage through the 
prism they will seem either to converge to or diverge from a 
point, which is the secondary focus: as the prism is turned, so 
as to change the first angle of incidence, the secondary focus 
will change. If the rays are strictly parallel, then, whatever 
be the position of the prism, the focus will not be altered. 
This, then, is a delicate test for ascertaining whether rays 
proceeding from the collimator are parallel or not. It remains 
to be shown how it can be converted into a rapid method to 
put the collimator into the right adjustment. 

The three fundamental equations for the passage of a ray 
of light through a prism, 


sind =nsing eh. (js os) 2) 
sind’ =nsin?’, _. «+ <\) sae 


f+ =O, . wo 

give | 
di’ COS 7 COS 7” 
di —s cos cos” “ 
In these equations 7 and 7 are the angles which the ray 
makes with the first and second surfaces_respectively on en- 
tering and leaving the prism; 7 and +’ the two corresponding 
angles of refraction, and a the angle of the prism. The right- 
hand side of equation (4) will, as a little reflection will show, 


z This shows 


that the greater the first angle of incidence the more nearly 
parallel are the rays. The following system of consecutive 
approximation will therefore give the desired result. 

Suppose the collimator is out of adjustment: move the 
telescope slightly out of position of minimum deviation ; then 
two positions of the prism exist which will bring the desired 
ray into the middle of the field. Call the position in which 
the first angle of incidence is greatest A, the other B. 

1, Put the prism into the position A, and focus the telescope 


steadily decrease when 7 is increased from 0 to 


Adjusting the Collimator of a Speetroscope. 97 


until the line in question, either dark or bright, is distinctly 
seen. 

2. Move the prism into position B, and focus the collimator 
until the same line is distinctly seen. 

3. Repeat the operation, always focusing the telescope 
when the prism is in position A, and the collimator when the 
prism is in position B. After three or four trials no change 
of focus is required; both collimator and telescope will then 
be adjusted for parallel rays. I find that it is by no means 
necessary to work much out of the position of minimum de- 
viation in order to gain a delicate adjustment. If the adjust- 
ment is made in the centre of the field, then I usually put the 
telescope into such a position that the line, when the prism is 
placed at maximum deviation, should just be out of the field 
of view; this gives quite a sufficient change of focus if the 
rays are not parallel on entering the prism. 

The following measurements, which were purposely made 
without special care, will show the accuracy of which the me- 
thod is capable. The sliding tube of the collimator was divided 
into millimetres. Two different adjustments for the sodium- 
line, made in the way described above, gave the readings 5:0 
and 4:0. The prism was now turned round so as to deflect 
the ray to the other side. Two adjustments now gave 4°1 and 
5°0. The mean of the four readings is 4°5. The adjustment 
was then made according to the well-known method of first 
focusing the telescope on a distant object and focusing the col- 
limator to the telescope afterwards: the reading was 4:2. As 
the focal length of the collimator was 300 millimetres, the two 
results differ only by a thousandth part of the focal length. 
Whether this difference is due to errors of observation, or 
whether it is produced by a difference in the focus of the yel- 
low rays and the mean visible rays, I cannot say; but I believe, 
with a little precaution, the method can be adapted to the 
study of the achromatism of a lens. 

I have assumed that the faces of the prism are perfectly 
plane. Practically it is difficult to get a prism in which this 
condition is accurately fulfilled; and it may be questioned 
whether the curvature of the prism may not seriously interfere 
with the accuracy of the method. ‘To this I reply :— 

1. That a prism which is known to be good may always be 
set aside to do this work. | 

2. That the reason of having the rays strictly parallel on 
entering the prism is based on the supposition that the faces 
of the prism are plane. _ It is by no means evident that parallel 
rays will give the best definition when the faces of the prism 
are curved, 


98 Prof. A. M. Mayer on the Laws of the 


3. That the change in the adjustment of the collimator in- 
troduced by the curvature of the prism is very small. One 
prism, which I know to be exceptionally bad, gave a differ- 
ence of a half per cent. in the focal length of the collimator. 
It is not the change of focus introduced by the curvature of 
the prism which makes the method inaccurate when the prism 
is bad, but the difference in the change of foeus in the two 
positions of the prism. This is one of the reasons why it is 
better to take the two positions of the prism not too far away 
from minimum deviation. The small displacement of the 
prism will only introduce asmall variation in the focal length 
due to the curvature of the faces. 


XIII. On the Morphological Laws of the Configurations formed 


by Magnets floating vertically and subjected to the Attraction 
of a superposed Magnet; with Notes on some of the Pheno- 
~ mena in Molecular Structure which these experiments may 

serve to explain and illustrate. By Aurrep M. MAyer*. 


ti the May Number (1878) of this Journal (page 397 of 


vol. v.), a short note was published on my experiments 


with magnets floating vertically and subjected to the attraction — 


of a superposed magnet. The object of this paper is to present 
accurate diagrams of the configurations formed by the floating 
magnets, and to give the laws ruling these configurations, 
with some notices of the peculiarities of these forms. At the 
same time I will show how neatly these experiments illustrate 
several phenomena in the molecular structure of matter. 

The Diagrams.—These diagrams show the configurations 
formed by numbers of magnets extending from two to twenty. 
They were obtained as follows:—The number of needles form- 
ing a configuration were floated in a bow] filled to its brim with 


water. The eye-ends of the needles, which protruded a short — 
distance beyond the tops of the corks, were of 8. polarity. A — 


cylindrical magnet, 38 centims. long and 15 millims. in diame- 
ter, was clamped in a vertical position, with its N. end at the 
constant distance of 60 millims. above the tip of the needle, 
which floated in the line of the axis of the magnet. I tipped 
the ends of the needles with printer’s ink; and when the con- 
figuration had formed and was stationary, I brought down 
upon the needles a piece of flat cardboard, and thus obtained 
prints from nature. Around each of the dots on the card- 


* Communicated by the Author. | 


Pe ar 


Configurations formed by Floating Magnets. 99 
board I drewa black disk. The centres of these disks I joined 


by lines, in order to bring before the eye the contours of the 
configurations. After the diagrams of the configurations had 
been obtained in this way, they were placed at-.a fixed distance 
from the camera ; and photo-engravings were thus made, of 
about one half the sizes of the original prints. 

The Morphological Laws of the Configurations——The confi- 
gurations made by the floating magnets form well-marked 
groups or classes, which may be designated in order as pri- 
mary, secondary, tertiary, quaternary, &c. The stable confi- 
gurations of one class form the nuclei to the succeeding 
ones. | 
Looking at the diagrams, the reader will see that figures 2 
to 8a inclusive form the primaries. Figure 8b begins the 
secondaries, for it is the hexagon with 2 for nucleus. Confi- 
gurations 8b, 8c, 9, 100, 10a, 11, 12, 138, 14, 15, 16, 17, 184, 
186, and 19a are secondaries, having respectively for nuclei 
the primaries 2, 2, 2, 2,3, 3,4, 4, 5a, 6a, 7,7, 7, 8a, 8a. 
The configuration 100 is not found in the diagrams; it is the 
same as the 10 which forms the nucleus of 20, only the two 
central lateral needles are further removed outward from the 
vertical axis of the figure 10. 

The group of 19 begins the tertiaries. Of these I do not 
give diagrams, but indicate their structure by giving the num- 
bers of the secondaries forming their nuclei, and then give the 
numbers of needles grouped around these nuclei. Thus, the 
structure of the configuration formed of 47 needles is indicated 
by 47=(18+14)+15; which means that 47 needles form a 
configuration which has 18 for its inner nucleus, surrounded by 
14 needles, and these in turn surrounded by 15; and as 18414 
forms the tertiary which is the nucleus to this quaternary 47, 
we enclose 18 and 14 in parenthesis. 

I here give the configurations to 51 inclusive, which form 
begins the quinaries. 

The configurations of the same number of magnets are let- 
tered a, b, c, to indicate their degrees of stability, a being 
always the most stable form. I have, however, lettered the 
configuration of 8 magnets in the order of their increasing 
areas, in order to make them serve better for the purpose of 
illustrating the phenomena of isomerism. Really 8¢ is more 


stable-than 8b. 


100 Prof. A. M. Mayer on the Laws of the 


nok 
Tato: 
ag 
1 @ 


Conjigurations formed by Floating Magnets. 101 


Prof. A. M. Mayer on the Laws of the 


102 
Tertiaries. 
196 = 9+4+10 25a =124+13 29a =16413 
20a = 9+11 200 hea 12 296 =174+12 
206 =10+10 26a =134+13 30a =174+138 
291la=10+4+11 266 =14412 306 =18412 
216 =11+10 27a =144+13 31 =18413 
22 =11+11 27b =15412 32 =18+414 
ae) = ee 28a =15413 33 =18415 
94a =12412 28b =16412 d4a =(8a+12)4 14 
246 =11+4+13 
Quaternaries. 

340 = (94+10)4+15 43 =(15+14)+14 

d9a = (9412)4+14 44 =(15+14)4+15 

306 =(10+12)+13 45 =(164+14)+15 

36 =(104+12)4+14 46 =(184+14)4+14 

o¢ =(104+13)4+14 47 =(18+14)+4+15 

88 =(114+13)+14 48 =(18+15)4+15 

89 =(114+138)+15 49 =(18+15)+16 

40 =(13+138)4+14 50 = (8+11415)4+16 

41 =(13413)+15 dla= (8+124+15)+16 


42 =(1384+14)+15 
Quinaries. 
516=(9+12414)+16. 


I do not say that the above list contains all the possible 

combinations. The listis more for the purpose of establishing 
the laws which I have already. formulated. 
In my first publication I gave two configurations for four 
needles :—one haying the needles at the corners of a square, 
and a stable form; the other unstable, and formed of a triangle 
containing a central needle. I have concluded that this form 
does not exist; at least its existence is so transient that it has 
never remained long enough for me to take a print of it. 

I have stated that 19) begins the tertiaries. This is an 
unstable configuration, and is formed of 9 surrounded by 10 
magnets. The other 19, 19a, is stable, and is formed of 8a 
surrounded by 11 magnets. It is to be remarked that not 
alone the tertiaries, but the configurations in the other classes 
begin with an unstable group of magnets. Thus 8¢ begins 
the secondaries, 19 6 the tertiaries, 345 the quaternaries, and 
516 the quinaries. : 

_ The reader has seen that a given number of magnets may 
form two or more different configurations. Thus five mag- 
nets form two, 56 a square with a magnet at its centre, and 


Configurations formed by Floating Magnets. —-108 


5aapentagon. Six magnets give 6a and 6b. With eight 
magnets we obtain three configurations, 8a, 8b, and 8e. Now 
the different configurations formed of the same number of 
magnets always exhibit different degrees of stability. Vibra- 
tion of the less stable forms (produced by alternately lifting 
and lowering the superposed magnet) sends them into the 
stable forms. Thus, 50 on vibration rearranges itself into 5a, 
6b into 6a, and 8c or 8b into 8a. With the configurations 
of higher classes (the tertiaries, quaternaries, &c.), even a 
knock on the table is sufficient to cause the needles of the un- 
stable configuration to move to positions of stable equilibrium. 

On looking at the diagrams, it will be observed that only 
the stable primaries form the nuclei of the secondaries ; and, 
moreover, those primaries which are not dimorphous, like 2, 
3, 4, and 7, serve as nuclei to more than one secondary. ‘Thus, 
2 is the nucleus of 8a, 8b, 8c, 9, and 106; 3 is the nucleus 
of 10a and 11; and 7 is the nucleus to 16, 17, and 18; while 
each of the other stable and dimorphous primaries, 5a, 6a, and 
8a, appears only once as nucleus, respectively to 14, 15, and 
18). This same power of the most stable nuclei to resist out- 
side stress is shown in the configurations of the tertiary and 
quaternary classes; where the secondary 11 appears as nucleus 
to 21, 22, 23, and 24. The secondary 18a persists in even a 
more marked manner asanucleus. This 18a has the contour 
of that very stable 7 (the only configuration possible with 7 
magnets) which forms its nucleus. Among the tertiaries 18a 
is the nucleus of 300, 31, 82, and 33; while in the quater- 
naries it forms the inner nucleus of 46, 47, 48, and 49. The 
fact of the persistence of these stable forms as nuclei may be 
suggestive to chemists and crystallographers. 

It is here to be remarked that (as a general rule holding 
good in all the classes), of two configurations made up of the 
same number of magnets, that configuration is the more stable 
which has the least number of needles for its nucleus. 

Illustrations of Molecular Structure. (1) Unstable Mole- 
cular Equilibrium.—That the molecules in a body may be in 
a state of unstable equilibrium so delicately balanced that a 
slight extraneous action of pressure, heat, light, &c. may 
cause a new molecular arrangement in the body, is shown in 
many facts. A few of the more familiar ones will answer for 
our purpose. Thus quiet water, which remains liquid at a. 
temperature of 10° C. or more below 0° C., changes suddenly 
into ice when agitated ; and during this solidification its tem- 
perature rises. In like manner a supersaturated solution of 
disodium sulphate solidifies when a crystal of this substance is 
dropped into it. Another instance of a sudden change from 


104 Prof. A. M. Mayer on the Laws of the 


an unstabie to a stable molecular condition is shown when the 
yellow crystals of mercuric iodide change, on the touch of a 
glass rod, to ascarlet colour, with a perceptible motion of their 
particles. These and similar phenomena are illustrated by the 
change of unstable to stable configurations caused by vibration, 
shock, and varying conditions of stress. Thus 50 changes 
into 5a, 6b into 6a, and 8¢ and 80 into 8a. 

(2) Illustrations of Expansion on Solidification, as shown 
by water, bismuth, antimony, cast iron, &c., are readily given 
by the floating magnets. One volume of water at 0° C. ex- 
pands, on freezing, into about one and one tenth volume of ice. 
It happens that the area of 56 is greater than the area of 5a 
by about one tenth; so that the increase in area which takes 
place when the pentagon of 5a is changed into the square 50 
may represent the increase in the volume of water when it 
changes into ice. 

It will be observed, on an examination of the diagrams, that, 
of two configurations formed of the same number of needles, 

that configuration which has the larger area has a magnet in 
its centre, Thus 50 exceeds in area 5a, and 6a is of greater 
area than 6b. Tosee the effectof a repulsive centre on a con- 
figuration, compare the areas of the two squares 4 and 56, and 
of the two pentagons 5a and 6a. The most marked effect of 
a repulsive central magnet is seen on comparing 14 with 15. 
The outside contour of each is formed of 9 magnets. The 
nucleus of 14 is the peculiar flattened pentagon, which is ex- 
panded into symmetry on the addition of another magnet, 
while at the same time the outside contour of 15 conforms to 
the regular pentagonal nucleus. These phenomena are so 
suggestive, that I make bold to put the question, May it not 
be that there is an actual centralization of atoms in the mole- 
cule when a body expands in solidifying, and in the case where 
of two or more isomeric bodies one has always the minimum 
density? I offer this as a suggestion which may be worthy of 
the consideration of crystallographers. 

(3) Illustrations of Allotropy and Isomerism.—The most 
interesting of our experiments with the floating magnets are 
those illustrating the phenomena of allotropy and isomerism. 
It is well known that an elementary substance may exist under 
very different forms. By the action of heat, electricity, &e. 
an element may have its physical and chemical properties so 
changed that no one would suppose that the different bodies 
thus made out of one and the same element were really all of 
the same substance. Yet the body remains elementary under 
the different appearances; for it is impossible by any means of 
subtraction to get any thing but the elementary substance 


Configurations formed by Floating Magnets. 105 


from it. Phosphorus, sulphur, and carbon give instances of 
allotropy. Thus graphite and the diamond are both carbon ; 
yet how different are they! One is soft, opaque, black, and 
with a metallic lustre; the other is the hardest of bodies, 
transparent, and resplendent by its refractive action on light. 
Graphite is a good conductor of electricity, crystallizes in 
small six-sided tables which belong either to the hexagonal or 
monoclinic system, and has a specific gravity of 2:2; while 
the diamond is a bad conductor of electricity, crystallizes in 
the monometric system, and has a specific gravity of 3°5. 
Whenever an element or a compound takes two different 
erystal-forms, these different crystals always differ in their 
density. 

These differences of form and density shown in allotropy 
and isomerism are well illustrated in the configurations which 
are formed of the same number of magnets. ‘Take figures 5a 
and 5b. The first is a pentagon; the second is a square with 
a magnet in its centre. The forces in these floating magnets 
and in the superposed magnet remain the same in all the con- 
figurations; and these have all been printed from needles floated 
in water whose surface was at a constant perpendicular dis- 
tance from the pole of the superposed magnet. Thus we see 


_ how the same atoms, endowed with forces of the same strength, 


may take different relative positions, and thus produce very 
different crystal-forms in the same matter. We may take 5a 
for an illustration of the atomic arrangement in the diamond, 
while 56 may stand for graphite. But there is always a 
change of density accompanying the different forms in allo- 
tropy ; and this fact is also illustrated by configurations 5 a and 
5b. In bodies formed of the same kind of elementary atoms, 
as in allotropy, it is evident that their relative densities will be 
directly as the number of atoms contained in the unit of 
volume. As our configurations illustrating allotropy contain 
the same number of magnets, it follows that the relative densi- 
ties of these configurations are inversely as their areas. Now 
the area of 5a (measured on the original prints) is 818 square 
millimetres, and the area of 56 is 992 square millimetres ; 
hence the density of 5a is to the density of 5b as 992 is to 
818. Thus we see how the arrangement of magnets in 5a 
may stand for the molecular structure in the diamond, while 
56 may stand for that in graphite. 

Numerous instances exist in chemistry of the same elements 
combined in the same proportions, yet producing bodies crys- 
tallizimg in different forms, and having different densities, 
colour, transparency, hardness, &c. As examples of this phe- 
nomenon of isomerism we may cite calcium carbonate, which 


106 Prof. A. M. Mayer on the Laws of the 


crystallizes in two forms, differing in density—viz. as cale spar, _ 


with a specific gravity of 2°72, and as arragonite, with a 
specific gravity of 2°93. Configuration 6a may stand for the 
molecular structure of cale spar, while 6) may stand for that 
of arragonite. The relative densities of these two configura- 
tions are as 208 to 247. 

A striking example of isomerism is given in titanic acid, 
which crystallizes in three distinct forms :—as anatase, specific 
gravity 3°82; as Brookite, specific gravity 4:02 ; and as rutile, 
specific gravity 4:25. These three isomers may be illustrated 
by 8c, 8b, and 8a, which have respectively the densities of 
382, 364, and 360. 

It will, of course, be understood that the above parallelisms 
are given merely as illustrations of how our experiments may 
serve to explain and illustrate the phenomena, on the assump- 
tion of the atomic hypothesis, and on the supposition that the 
actions which, in the experiments, take place in a plane, may 
similarly take place among repelling and attracting points 
situate in space of three dimensions. 

Other forms of the Experiments.—Instead of floating the 
magnets, they may be suspended by fine silk fibres. In this 
method of experimenting the attractive action of the super- 
posed magnet is replaced by the action of gravity, which 
draws the mutually repellant needles towards the vertical. 

An advantage of this form of the experiment is that the 
configuration can be transported, and may thus serve in illus- 
tration of a moving molecule as set forth in the kinetic 
theory of gases. It is interesting to watch the mutual actions 
of two or more approaching configurations, and to observe 
the motions in the exterior and in the contour of a suspended 
configuration on its impact against a resisting or a yielding 
surface. | 

Professor O. N. Rood suggested to me to replace the sus- 
pended magnets by gilded pith balls, hung by silk fibres and 
similarly electrified. 

Professor Frederick Guthrie, under date of May 21, 
writes :—“ If the corks are made somewhat wider than in your 
larger needles, the needles move and arrange themselves very 
quickly if they are turned over and floated on perfectly 
pure and freshly filtered mercury. Those which reach the 
edge incline with their corks in the capillary trough.” 

Method of projecting the magnified Images of the experiments 
on a Screen.—To exhibit these experiments before a large 
audience it is best to use short magnets made as follows :— 
Magnetize rather large sewing-needles, with their points all of 
the same polarity ; then take each needle between the flat jaws 


i ech eed nha ep dell a 


Configurations formed by Floating Magnets. 107 


of a pair of pliers, and with a pair of cutting-pliers snap off 
the needle close to the jaws of the other pliers. Thus form a 
series of magnets about 3 inch in length. Run each of these 
through a thin section of a small cork, and then coat both 
needle and cork with shellac varnish. Float these magnets in 
a glass tank placed over the condensing lens of a vertical- 
lantern ; or you may even float them directly on the condenser 
itself, if this is made of an inverted glass shade filled with 
water. This form of condenser was first used by Dr. R. M. 
Ferguson, of Edinburgh. 

Figure 1 shows the arrangement of the experiment. The 
rays of light, R, from a heliostat, or from an oxyhydrogen light, 


fall on an inclined mirror, A, placed under the water con- 
denser, C. The needles float on the surface of the water in 
this condenser. The rays which have passed through the lens, 
L, are reflected by the swinging mirror, B, to the distant 
screen, where they form the images of the floating magnets. 
The magnet is held over the needles at M by means of a wire 
which is wrapped round the magnet to serve as a handle. If 
a long magnet be used, it will work well if its pole is brought 
over the needles* by inclining it. - 
These experiments with floating magnets give forcible pre- 
sentations of the reign of law. It is indeed quite impressive 
to see order being evolved out of chaos as we hold a magnet 


* The magnetic needles in the experiments may be replaced by pieces 
of soft iron wire, which will be magnetized by the induction of the super- 
posed magnet. 


108 On a Condenser of Variable Capacity. 


over a number of needles carelessly thrown on water, and 
witness them approaching and, one after the other, entering 
into the structure of that geometric figure which conforms to 
the number of magnets composing it. 


XIV. A Condenser of Variable Capacity, and a Total-Reflexion 
Experiment. By OC. V. Boys, A.R.S.M., Lecturer for the 
Term on Natural Science at Uppingham School*. 


ISHING to show my pupils the effect of condensation 

on the spark, I thought a condenser the capacity of 

which could be reduced gradually to nothing would be most 

suitable. So I made this simple contrivance, which answered 
its purpose well :— 

A glass tube is sealed at one end and is covered with tinfoil 
for one third of its length; this forms the outer coating. The 
inner coating consists of a test-tube with the rim cut off, also 
covered with tinfoil ; this is fixed to a wire, and can be drawn 
in and out. When it is fully in, the condenser has its maxi- 
mum capacity ; when drawn out as far as possible, the two 
coatings are too far apart to have any sensible action, and the 
capacity is zero. 

On hanging this on the conductor of a Holtz machine the 
effect on the spark is well shown. Let the wire be first pushed 
in as far as possible, the condenser then acts to its full extent ; 


but on gradually drawing it out the sparks are less and less _ 


bright, but follow one another more and more rapidly, till at 
last, when it is fully out, they have passed gradually to the 
almost continuous pale spark so characteristic of a Holtz ma- 
chine. To show the effect best, the poles should not be more 
than about half an inch apart. Of course much ozone is 
formed inside the tube. 


The total-reflexion experiment was an accident. A small 
condenser made of a test-tube gave way under the strain, a 
minute hole being pierced in the bottom, through which sparks 
passed almost continually. No light could be seen anywhere 
except on the rim of the tube, which formed a brilliant circle 
of light. The light from the spark was totally internally 
reflected in the substance of the tube till it reached the rim, 
which it struck normally. The bright circle of light (the tube 
itself being dark) was very striking ; and thé experiment is a 
far truer illustration of total internal reflexion than the more 
beautiful one with a stream of water. The tube is, unfortu- 
nately, broken; and I have not succeeded in piercing another 
with the spark. A crack made with a hot wire does not doso well. 

* Communicated by the Physical Society. 


ee 


Beloec, 


XV. Theory of Voltaic Action. By J. BRown*. 
Boe the publication of a former paper on this subject f 


the apparatus employed in the bimetallic-ring experi 
ment has been much improved by using a finer suspension-wir 
(001 inch diameter) for the needle, and electrifying it by 
means of a Daniell’s battery of 100 cells. Hach cell is made 
of a 4-in. x 2-in. test-tube, with the copper at the bottom 
surrounded by copper-sulphate crystals, and connected by 
gutta-percha-covered wire with the zinc of the next cell. The 
space between the coppers and zines is filled with sand satu- 
rated with weak solution of zinc sulphate; and zinc filings are 
mixed with the upper layers of sand to reduce any copper 
sulphate tbat might diffuse upwards. The cells are mounted 
in an ebonite stand. With this arrangement and the copper- 
iron ring described beforef, it is quite easy to get decided de- 
flections of about 3 centims. in air, copper negative to iron. 
After admission of the hydrogen sulphide the deflections are 
considerably greater, copper being now the positive metal. 

As copper is negative to nickel in water and positive to it 
in hydrochloric acid, a ring was made of these metals similar 
in size to the copper-iron one. Here the deflection obtained 
was about 4 centims. in air, copper negative. Hydrochloric 
acid gas was caused to flow into the case; and after a few 
oscillations the negatively electrified needle crossed zero and 
turned towards copper, the deflection gradually increasing to 
15 centim. The flow of gas was then stopped ; and the deflec- 
tion slowly decreased. In four hours after, it had fallen to 1 
millim. Itthen began to increase; but the admission of fresh 
hydrochloric acid gas caused it to diminish, a phenomenon the 
explanation of which is not clear. The reversal of the poten- 
tial of these metals, on the admission of the gas, however, was 
quite decided. The experiment was not repeated, as the cor- 
roding action of the acid was destructive to the apparatus. 
The ratio of differences of potential given by these deflections 
is, of course, rough, as the apparatus is not adapted for exact 
measurements. 

In a simple voltaic cell, consisting of a copper and a zine 
plate in connexion and immersed in an oxidizing electrolyte, 
the current due to the chemical action in the cell flows in the 
electrolyte from zinc to copper. If, then, we divide the elec- 
trolyte by a non-conducting plate, positive electricity ought to 
accumulate on the side of the plate towards the zinc, and 


* Communicated by the Author. 
+ Phil. Mag. August 1878. 


Phil. Mag. 8. 5. Vol. 7. No. 41. Feb. 1879. K 


110 Mr. J. Brown on the Theory of Voltaic Action. 


negative on the side towards the copper. In order to prove 
this, a disk of thin vulcanite, with a hole 
in its centre and a radial slit, cd, had two 
paper segments, a and 0, fixed onit. These 
were moistened with water, and the whole 
placed in the apparatus described before in 
the same position as one of the bimetallic 
rings. The needle was set over the slit cd; 
and each of the points a and 6 of the paper 
segments was in connexion with a slip of 
moist blotting-paper which passed out of the case. The outer 
ends of these slips lay. side by side on a plate of vulcanite. 
Touching either one of them with a piece of zine or copper, or 
with one end of an insulated copper-zinc pair soldered together, 
had no appreciable effect on the electrified needle; but when 
the zinc end of the pair was placed on one slip and the copper 
end on the other, the index light-spot at once deflected about 
10 centims., showing the paper in connexion with zine posi- 
tive. When a copper-iron pair was used the iron side was 
positive; but on placing a drop of potassium sulphide at the 
junction of the copper and damp paper, the copper side became 
positive. Ifthe copper-iron pair, instead of being soldered 
together was joined by a drop of water, no deflection occurred, 
or only a very small one; but the addition to the connecting 
water-drop of a small quantity of potassium sulphide caused 
a vigorous deflection of the needle, the segment in connexion 
with the copper being now negative on account of the current 
flowing across the connecting drop from copper to iron. 

The slit ed corresponds to the dividing plate in the electro- 
lyte; and if we suppose this plate to be air and its thickness 
to be increased, replacing the liquid till nothing but a mere 
film remains on each metal, we have then the conditions of 
Volta’s condenser experiment, where, the plates being close in 
front of one another and in metallic connexion, the film of 
condensed moisture &c. on the zinc plate has on its outer sur- 
face a positive charge, that on the copper a negative, the layer 
of air between them preventing the combination of the two 
electricities. It may be urged that the better the plates of a 
condenser are ground or fitted together, the more apparent is 
the contact effect; but it is scarcely to be supposed that we 
have yet had any experiments with plates so well surfaced that 
it was certain no air layer was present between them, or so 
well mounted that they could be kept exactly parallel while 
being separated, all points on their surfaces separating at the 
same instant. 

In my former paper, the production of a difference of elec- 


a a 


Effect of the Motion of the Air within an Auditorium. 111 


tric potential by contact of dissimilar substances is attributed 
to the nature of the gas or atmosphere surrounding them. It 
is probably so only in so far as such gas produces, by conden- 
sation, a film of itself on the surfaces of the substances i 
question. . 

In experiments where the difference of potential of a metal 
and a liquid in contact is the subject of investigation, the 
arrangement is probably analogous to a two-fluid cell with 
plates of the same kind of metal, 7. e. the metal under exami- 
nation—one of the fluids in the supposed cell being that in 
contact with the metal, and the. other being the film of mois- 
ture &c. condensed on the metal. 

Slight variations in the nature of this film, due perhaps to 
the remains of whatever may have been used for cleaning the 
metal, or to such vapours as might be present in the atmo- 
sphere of the laboratory, would produce corresponding varia- 
tions in the amount of difference of potential observed—just 
as a small quantity of hydrogen-sulphide in the atmosphere 
surrounding the copper and iron in contact reverses the rela- 
tive potentials of these metals. This would no doubt account, 
at least partially, for the discrepancies in the results obtained 
by different observers, and indeed by the same observer in 
different experiments with the same liquid and metal. 

Belfast, December 1878. 


XVI. Lfect of the Motion of the Air within an Auditorium 
upon its Acoustic Qualities. By W.W. JAcQueEs”. 


i Bs is the purpose of this paper to give an account of some 
experiments made for the purpose of determining the 
effects of the currents of air within an auditorium upon its 
acoustic qualities. These experiments are in three series:— 
the first being a laboratory investigation into the effects of 
currents of air upon a ray of sound; the second and third, 
studies, by different methods, of the effects of the currents of 
air in a lecture-hall and a theatre, upon the waves of sound. 
Since the air of a hall is the medium by which sound is con- 
veyed from the speaker or singer to the hearer, it would cer- 
tainly seem of fundamental importance that this air should be 
in the condition best suited to the propagation of sound. 
Hxperiments made by the author, in a considerable number of 
halls, show that the atmosphere is almost invariably disturbed. 
by currents of air of varying density crossing the room in all 
directions. These currents have been traced out with thistle 


* A reprint from the Journal of the Franklin Institute, December 1878, 
communicated by the Author. 


K 2 


‘112 Mr.W.W. Jacques on the Effect of the Motion of the 


balls, and their velocity measured with the anemometer. The 
estimates of density have been made from the velocity of mo- 
tion. Now the experiments of Professor Tyndall have shown 
that currents of air of varying density form one of the chief 
obstacles to the propagation of sound-waves. The author, in 
repeating these experiments in a somewhat modified form, 
found that such currents of air not only decrease the intensity 
of a sound-wave, as Professor Tyndall has shown, but that 
they actually modify its form, and so give rise to great indi- 
stinctness. The experiments were made as follows:—At A 
was placed a source of sound, | 


A+—+—-+—-—4-+8,. 


being in some cases an organ-pipe, in others a man who spoke 
in a clear and distinct voice, and in others various musical 
instruments on which simple combinations of notes were 
played. Just below the points + + &c., were placed sub- 
stances heated to such temperatures as to give rise to currents 
of air corresponding in density to those found in an auditorium. 
At E was placed the ear, which, though it be not so reliable 
an instrument as the singing-flame of Professor Tyndall for 
estimating intensities of sounds, is, of course, the best instru- 
ment imaginable for determining their qualities. The results 
of the experiments were as follows :—The ear being placed at 
i, and a small lead organ-pipe, blown with a constant pressure 
of air, at A, the heated bodies were placed under + +, &c. 
A very decided decrease in the intensity of sound was noticed; 
but it was also noticed that the previously clear note lost its 
distinctness. The pipe was removed, and a man was placed 
at A, who spoke in clear and well-defined tones. ‘The effect 
was not only to decrease the intensity of his voice, but to make 
it shghtly confused and indistinct, as if each syllable were re- 
peated several times in very close succession. When a flute 
was substituted for the voice the effect was the same. The 
effect on a violin seemed to be considerably less. Witha drum 
no effect whatever was observed. The effect seemed to be 
most marked on the man’s voice, or a musical instrument in 
which the overtones were comparatively small. The explana- 
tion of this is very simple. ‘The original ray of sound, striking 
upon the first current of air, is partially reflected and partially 
transmitted. The loss of the reflected portion causes a de- 
crease in the intensity of sound. The transmitted portion, 
striking upon a second current, is likewise divided, and its 
transmitted portion continues to be so divided as many times 
as there are variations in the density of the air. Its reflected 
portion, as well as that of all the succeeding reflections, instead 


| 


Air within an Auditorium upon rts Acoustic Qualities. 113 


of being wholly lost, is interrupted in its backward course by 
the first current of air and reflected along the path of the 
primary wave, but following it at an interval of time depend- 
ing upon the thickness of the current of air. Hach reflection 
being thus again and again reflected and divided, we have, fol- 
lowing close upon the primary wave, a multitude of secondary 
waves, which, falling upon the ear, greatly mask the distinct- 
ness of the original sound. Currents of air of varying density 
then cause, first, a decrease in intensity of sound, and secondly, 
an indistinctness or confusion of the sound. 

That currents of air, which we have thus studied in the labo- 
ratory, act in the same way in an auditorium may be shown 
by the following experiment, in which the sound-waves may 
be actually traced out in space, and their confusion, conse- 
quent upon the introduction of currents of air, likewise shown. 

Near the middle of a lecture-hall, 92 feet long and 65 feet 
wide (the hall of the Massachusetts Institute of Technology in 
Boston), a heavy plank, 6 feet wide and 12 feet long, was set 
on one end and firmly fixed. Hight feet from its middle point, 
on one side, was placed a B 4-stopped lead organ-pipe, which 
was so connected with a gasometer as to be blown with a con- 
stant pressure of air. 

On the other side of the plank and within the sound-shadow 
a system of coordinates, in a plane parallel with the floor, was 
established by means of light wooden rods, which ran parallel 
and perpendicular to the board, and their length divided into 
centimetres. 

Now it has been shown by the author (Proc. Amer. Acad. 
Arts and Sciences, May 10, 1876) that rays of sound diver- 
ging from such a source, and being diffracted around the edges 
of the board, will, when they meet each other, after having 
passed over paths differing by a half wave-length, neutralize 
each other and produce comparative silence. By moving a 
B 4 resonator, connected by means of a rubber tube with the 
ear, along these coordinates the points of interference are easily 
detected, and are found to be situated as predicted by formulee 
similar to those used in the diffraction of light. In fact the 
cases are entirely analogous. 

We have here, then, a means of mapping out the positions 
of the sound-waves in space, and can say that at one point 
there is silence because two sound-waves have met, crest upon 
the trough, and neutralized; at another the sound is loud, 
because two waves have met, crest and crest, and trough and 
trough, and have doubled. All this is true so long as the air 
of the hall is at rest; and these experiments have been made 
with doors, windows, and registers carefully closed. 


114. Mr. W. W. Jacques on the Ejfect of the Motion of the 


Every thing being in this condition and the sound-waves 
ising been mapped out, the doors and windows were thrown 
open to the winter’s air, and the registers were opened to 
admit as many streams of air heated to nearly 100° C. What 
is the effect? Currents are rushing about the hall in every 
direction (we have the conditions of the laboratory experi- 

ment); the waves of sound are superimposed by numberless 
reflections whose points of condensation do not coincide; and 
the phenomena of diffraction instantly disappear. This ex- 
periment was many times repeated, and always with the same 
results. 

Ts is evident, then, that in order to procure the proper pro- 
pagation of sound we must do away with these air-currents. 
Tt must be remembered, however, that when large numbers 


of persons are crow ded into halls, the air within is usually ~ 


subjected to very considerable disturbances in order to obtain 
even indifferent ventilation. How, then, shall we obtain the 
desired ventilation and at the same time prevent the formation 
of currents of air? 

The solution of this problem seems to me to be given in the 
third series of experiments, which were carried out in the 
Baltimore Academy of Music, designed by Mr. J. Crawford 
Neilson, architect, of that city. 

The ventilation of this house is so arranged as to prevent 
largely the formation of air-currents of unequal density. Ac- 
cording to a survey, made with thistle-balls and the anemo- 
meter, of the space contained within the walls of this theatre, 
the movement af the air is as follows :— 

The whole supply of fresh air is admitted at the back of the 
stage, is there warmed, then crosses the stage horizontally, 
passes through the proscenium, and then, somewhat diagonally 
towards the roof, across the auditorium in one grand volume 
and with gentle motion so as to almost entirely prevent the 
formation of minor air-currents. It is exhausted partially. by 
an outlet in the roof and partly by numerous registers in the 
ceilings of the galleries. From this central outlet and from 
the large flues of the registers the air passes into the ventila- 
ting-tower over the great chandelier, which supplies, in its 
heat, a part of the motive power of the circulation. It is 
further expelled from the tower by means of large valves so 
contrived that, while they offer no obstacle to the egress of air, 
they completely deny té entrance. The amount of air so passed 
through the house is, as determined by a series of experiments, 


about fifteen thousand feet per minute. This amount, suffi- 


cient to ventilate the house, is just what seems to be required 
to impress the proper moyement on its atmosphere. That it 


: 
| 


4 
—— 


Air within an Auditorium upon its Acoustic Qualities. 115 


is amply sufficient for ventilation is shown by the fact that the 


thermometers of the upper circle do not vary perceptibly from 


those of the orchestra circle. 

The seating-capacity of the house is about sixteen hundred 
persons. The acoustics are, if we may judge from the testi- 
mony of a large number of singers and speakers, as well as 
from our own observation, among the best. 

The weakest voice is audible to every seat in the house; 
sounds such as a sigh, a kiss, or even the simulated breathing 
of the somnambulist, may be heard in the most distant parts ; 
and all effects in music are exactly rendered. All singers and 
speakers agree in describing the facility with which the voice 
is used on this stage. 

It now remains to show that the universally acknowedged 
acoustics of this house are largely due to the condition of the 
air, and not to the arrangement and material of the walls, 
together with other well-known causes of success or defect. 
For this purpose persons have been repeatedly stationed at 
different parts of the house during a performance, without 
being informed of the nature of the experiments to be carried 
out. They have simply been asked to note, at intervals during 
the evening, the comparative ease with which they could hear 
the performers. At various intervals during the evening the 
valves which control the ventilation were reversed, so as to en- 
tirely interfere with the unbroken condition of the air and give 
rise to currents of circulation. Almost invariably the testi- 
mony of the hearers would be that, at times corresponding to 
the interruption of the ventilation, the ‘‘ sound was dead,’ was 
“ confused and indistinct;’’ and it would be observed that 
people all over the house would make an effort to listen. As 
an example of these experiments, the following is copied from 
the author’s notes, for the evening of January 24, 1878. 

There was a concert, consisting of orchestral music and solos 
held in the house. At8 o’clock observers, A, B, C,and D, were: 
stationed respectively in the orchestra, right and left wings of 


_ the balcony, and on the bridge that spans the stage above the 


level of the highest proscenium boxes. They were entirely 
ignorant of the nature of the experiment, and were simply re- 
quested to note the times of good and bad hearing. 

At half-past eight o’clock the valves were reversed and 
remained so till nine, when they were again set aright; after 
the performance the following testimony was given by the 
different observers :-— . 

A. Orchestra—to 9.15, very indistinct; 9.15 to 10, much 
better. 


116 Effect of the Motion of the Air within an Auditorium. 


B. Right baleony—8. 45 to 9.15, sound was dead; 9.15 to 
10, decidedly better. 

C. Left baleony—8 to 8.40, good ; 8,40 to 9.15, confused ; 
9.15 to 10, good. 

D. Over stage—8 to 8.30, good; 8.30 to 9, strong draught, 
hearing better; 9.10, dr aught disappeared. 

An examination of this Table shows that the observers in 
the auditorium found a period of half an hour’s duration when 
the sound was not so plain as it had been before, or was after. 
This time was of the same length, but from 10 to 15 minutes 
later than the period of interruption of the ventilation ; but 
some time is, of course, necessary for the air-currents to form, 
or, being formed, for them to be destroyed. 

The observer (D) over the stage, however, found the hear- 
ing better during the half hour of interruption; and this is 
exactly what would be expected, for the interruption of the 
current of air through the auditorium causes it instead to rise 
directly over the stage into the large space in which hangs 
the scenery, and thence out of the building. 

During Neilson’s performance of ‘ Rosalind,” observers A 
and B were stationed in the first, and C and D in the second 
balcony from 8 to1l0 p.m. At 8.50 o’clock the ventilators 
were closed and the lobby doors, together with those leading 
from the lobby to the street, were thrown open. 

Thistle-balls let loose from the balconies showed currents of 
air coming in at the doors and crossing the auditorium towards 
the stage. At 9.20 the doors were closed and ventilating- 
valves set aright. The testimony of the observers was as 
follows :— 


A. First balcony—8 to nearly 9, good; for about an hour, . 


bad; afterwards, much better. 

B. First baleony—8 to 9, good; 9 to 9.30, bad; 9.30 to 
10, good; strong current of air felt from the door a little 
before 9. 

C. Second baleony—8 to 8.50, good; 8.50 to 9.20, bad ; 
9.20 to 10, good. 

D. Second baleony—8 to about 9, good; 9 to 9.20, bad; 
9.20 to 10, good. 

In the foregoing paper we have studied the effects of air- 
currents upon the acoustic qualities of an auditorium. That 
this is only one of the factors on which success depends the 
author knows full well; and experiments are now in progress 
upon some of the other causes which modify the acoustic pro- 
perties of churches, theatres, and halls. 

These, however, have been in part studied before, while the 
above researches are believed to be entirely new. 


: 


| 


Prare} 


XVII. On the Music of Colour and Visible Motion. 
By Professors JoHN Perry and W. H. Ayrron*. 


[Plates V. & VI.] 


7 the present time, when musical instruments of one form 

or another are employed nearly throughout the whole 
world, when even the emotions evoked by the sounds of the 
human voice have given life to the efforts of a whole nation 
in the ‘ Marseillaise,’ we are apt to forget that our feelings 
may be excited through other mediathan sound. But, just as 
now all kinds of musical instruments are used in rendering 
the works of great composers, so we may expect that all known 
methods of exciting emotion will be combined in the grand 
emotional compositions of the future. 

Although our feelings may be worked on through the me- 
dium of any of our senses, one only of these has been hitherto 
eultivated in the highest degree. And the reason of this is, 
that there exists an infinite number of easy ways of producing 
sound; so that combinations of sound have been used as the 
vehicle for exciting emotion in us, and in our forefathers, for 
the last four hundred years; and, as a result, the ear has been 
slowly trained to act as the conveyer of the varied impres- 
sions it is the province of the artist to create, whereas the 
means in our power of acting through the eyes are even up to 
the present day clumsy and inadequate. 

Of the optical methods hitherto employed to work on the 
emotions, the oldest is certainly sculpture ; but this can never 
create an emotion unconnected with thought; and the feelings 
produced by it vary much in different people, and even in the 
same person at different times. The musical composer, on 
the other hand, is able to produce a definite succession of 
emotions which he can vary at will, and which are not utterly 
different in different people. A piece of sculpture is but sug- 
gestive—it merely introduces some simple emotion which acts 
in a controlling way upon the human mind; so also a fine 
picture induces a dreamy state and sets one a thinking. 

Other emotions, again, are excited in particular people by 
certain associations connected with a taste, smell, &c.; but 
these may be likened to the energy stored up in gunpowder 
or nitroglycerine, to be set free by the smallest accident, 
whereas the efforts of real emotional art may be likened to 
those of which the effects may be calculated according to 
known laws. 

Tor the eye to act as an agent for the emotions, it must 


* Abstract of a paper read before the Physical Society, November 23rd, 
878, 


118 Professors Perry and Ayrton on the Musie 


receive much cultivation. Even with the experience of sound 
the ear has gained during the last four hundred years, how 
very few people are there sufficiently educated to have their 
- feelings excited through music in answer to the emotions of 
a composer ? and how pleasing to all is the repetition of a strain 
in a melody or the movement in a dance, perhaps from the 
instantaneous education the ear or the eye receives which en- 
ables it to better understand the movement when repeated. 
Consequently, if we consider the cumbrous and expensive 
nature of the apparatus necessary for producing regular 
changes of colour, or of motion, or of the size of the moving 
bodies, we may expect that it will probably take a long time 
before the world is able to employ our more complicated 
agencies. 3 
- It may appear at first sight that in placing motion on a 
footing of equality with what we consider its sister graces— 
sculpture, painting, and music,—we offered an indignity to 
these latter ; and it may appear inconceivable to many how any 
amount of study of moving bodies can ever create an art as 
powerful and as enchanting as music. But it must be borne 
in mind that our present form of the fine arts probably only 
owes its existence to the accident that western nations have 
more assiduously educated the emotional side of their minds 
in certain particular directions ”*. 

And in our own country we have aclose connexion between 


the varied emotions created by colour or movement and those © 


excited by sound. It is well known that when certain per- 
sons hear an Oratorio, an Opera, or even a well-played violin 
solo, they see, without any voluntary effort on their part, 
beautiful changing mosaics, the patterns of which have defi- 
nite connexions with the musical chords, and that such people 
always see a flash of light when they hear a sudden shriek of 
a railway-whistle. 

The emotions excited by large bodies having a great velo- 
city do not seem to be producible by any thing else in nature. 
These are felt when we stand ona bridge over a railway when 
a train approaches and passes underneath at great speed, or 
when we stand at the side of a railway when the train passes, 
even if we hear no sound, or if there is no appreciable trem- 
bling of the earth. Jn our first experience of such visible 
motion, terror, due perhaps to its utter strangeness, predomi- 


* Here followed a number of examples taken from the Japanese stage and 
musical performances, proving that great conventionality existed among 
different nations in the expression of the emotions, and. lending weight 
to the doctrine that music, unlike painting, received no suggestion from 
nature, and was therefore a creation of each individual people. 


~~ PS ee 


of Colour and Visible Motion. 119 


nates. Similarly, the emotions produced by the play of 
colours in a fine sunset, by the rolling of the waves on the sea- 
shore, by the rhythmic motion of a large engine or of a long 
pendulum, by the tracing out of the combined harmonic curves, 
which have now become well known to all who have heard 
lectures on vibrating bodies, seem to be quite different from 
one another, and from the emotions produced by sound. 

We have therefore tried to make a machine which to the 
emotions produced by a combination of colour, a mass in 
motion, and by motion in curved paths, would bear the same 
relationship as a musical instrument to music. We have not 
ventured to give our machine a name, since the name of the 
instrument should be that of the art; and although we have 
a name for exciting emotion by sound (music), we lack names 
both for the art of exciting emotion by colour, and by moving 
bodies. ; 

Many instruments have already been devised for combining 
together two harmonic motions; but as the conception of using 
such machines as emotion-exciters has never been present in 
the designers’ minds, the performances of these instruments, 
although very beautiful, are necessarily of a comparatively ele- 
mentary nature. The most important of these machines, all of 
which, with the exception of one or two Prof. Guthrie has been 
so very kind as to have arranged in working order before us, 
are Blackburn’s pendulum, Wheatstone’s kaleidophone, Lis- 
sajous’ tuning-forks, Yeates’s vibrating prisms, Donkin’s har- 
monograph, Tisley’s and Spiller’s harmonograph, and Hopkins’s 
electric diapason. In some of these, as in Blackburn’s pen- 
dulum, only one particular pair of harmonic vibrations can be 
combined, and any change in the period of either means a stop- 
page of the instrument, corresponding in music with a delay 
in the tune at the end ofevery chord ; in others we can change 
the period of one or other of the component harmonic vibra- 
tions, but have no certain means of controlling the amplitude, 
which in music would be equivalent to an inability to render 
at will a note forte or piano; or, rather, as it is not only the 
strength of the entire note, but even the amplitude of the 
various component harmonics that these instruments cannot 
regulate, it would be as if in music there was the probability 
of a note marked in the score as piano for the flute being ren- 
dered by a loud blast on the trumpet. In only one of these 
harmonic-motion compounders with which we are acquainted, 
viz. in the most perfect of the existing ones, Tisley’s harmo- 
nograph, can an elliptic and a linear motion be combined; 
but even in this case a change from this motion to any other 
can only be made by first stopping the machine; and in none 


120 Professors Perry and Ayrton on the Musie 


of the machines can a sudden change be produced in phase. 
Now it is obvious that we require a motion-producer of far 
greater range than any of these, if we are to play on the 
emotions, since all the qualities—elation and depression, velo- 
city, intensity, variety, and form (which it is considered are 
possessed by a complex emotion )—must be visibly rendered. 
The result produced by our instrument is this:—A round 
shadow is thrown upon the plain white wall of the room in 
which the audience are seated. The shadow appears to be a 
large black ball, of which the size during the performance may 
be made to vary. It has motions over the wall which are pure 
harmonic or combinations of harmonic motion, produced by 
our being able to give to the shadow two independent motions 


—one in a vertical line, the other in a horizontal line, each con-. 


sisting of a combination of linear harmonic motions, the ampli- 
tude, period, or phase of any one of which may be varied at will. 
We give a collection in figures (A to U, Plate V.) of some of 
the most simple paths traced out by our moving ball, and which 
differ from the ordinary Lissajous’ figures in that we have 
placed little circles at such distances asunder as are passed 
over in equal times, in order to give an idea of how the velocity 
varies at different parts of any such path. Unfortunately, 
however, for giving a conception of the appearance, it is this 
variation of velocity, the effect of which on the senses no figure 
or description can give any idea, which constitutes one of the 
most striking features of the exhibition. Many of our readers 
will, however, have seen the motions of a very large Black- 
burn’s pendulum, and of a very long simple pendulum; and 
they will therefore have gained such an idea of the motions of 
which we speak as a person, who has heard only the chirp of a 
sparrow, has about Beethoven’s sonatas. 

It must be remembered that while all the possible paths of 


the moving body are beautiful in shape, they are also endless © 


in their variety. Not only may they vary without limit in 
their form, but also in their size, and in the velocity with which 
the body moves along them. Thus, perhaps the body is swing- 
ing slowly in a straight line in any direction, like the swaying 
of a huge tree in the wind, or so rapidly that a dark line only 
is visible, when, touching a key, the line is suddenly seen to 
open out, and the body rolls round a small or great circle, or 
a small or great ellipse of any proportions and with any velo- 
city*; or the figure may be like any of the simple figures 


* One of the most beautiful things in connexion with the recent monster 
captive balloon in Paris was its rolling round and round in the breeze, 
like a huge inverted conical pendulum, after the stay ropes had been 
liberated, just before its ascent. 


a 


- of Colour and Visible Motion. 121 


illustrated in the diagrams, or any others of the millions of 
different and. more complicated forms producible. Some may 
change all their dimensions gradually in a certain direction, 
while dimensions in the other directions remain unchanged ; 
others may alter all their dimensions in different directions 
simultaneously, but with different velocities. Now, as we gaze 
at the body with all these graceful complex motions, which can 
readily be varied in shape or size of path, or in velocity of 
description, the same sort of awe comes over us as must have 
been felt by the people when they first listened to the strains of 
the earliest musical instrument. 

To be sure it can never be as easy to change from a grave 
circular swing toa quick and complicated motion as it is to put 
down the key of a pianoforte; and it may be long before me- 
chanicians will be able to let us vary the motion with sufficient 
rapidity. But we found that we could, even with our imper- 
fect instrument, change one form of motion to almost any 
other possible one in about a second; and this is sufficiently 
quick for the present educational state of the art. 

Our instrument itself we unfortunately cannot show, as it 
is the property of the Japanese Government, and is in Japan. 
Some photographs, however, of it and of our assistants who 
took part in its construction and performances are lying on 
the table. The exhibitions have been confined to ourselves 
and our students ; but it was our intention, after we had edu- 
cated ourselves by practising with the machine, to exhibit it 
publicly. Unfortunately, however, from various delays con- 
nected with improvements and alterations necessarily con- 
nected with the designing of such a new machine, it was 
hardly completed before one of the present writers left Japan, 
and the other has now no opportunities to practise with it. 
But it is our intention to construct a new instrument with 
many improvements on the first model, one of the most im- 
portant being the carrying out of the idea we had at the com- 
mencement, of enabling the operator, by touching keys, to 


give any desired brilliant or sombre coloration to the wall 


on which the shadow of the body is moving, or to play on the 
wall a changing mosaic. 

_ We will now describe the simplest form of our instrument, 
represented in fig. 1 (Plate VI.) about one sixteenth of its 
full size. 

B C is aroller which is turned by a handle D (not visible in 
the figure), the fly-wheel Ei being of use in steadying the 
motion. ‘The roller is divided into three portions, BF, F G, 
GC, by the circular collars at F and G; at H, J, K, the 
centres of these portions, the section of the roller is circular, 


122 Professors Perry and Ayrton on the Music 


whereas at any other place it is such that, acting like a cam 
or tappet, it gives pure harmonic motion to a slider kept press- 
ing on the roller, and only capable of radial motion. Such a 


sliding piece, resting any where between K and C, receives one 


complete harmonic motion during one revolution of the roller ; 
if it rests anywhere between G and K, it completes two pure 
harmonic motions during a revolution, three between J and 
G, four between F and J, five between H and F, and six 
between Band H. The amplitude gradually decreases as the 
sliding piece is made to rest on places nearer the circular sec- 
tion, where of course there is no up and down motion of the 
sliding piece. 

livery section, therefore, of the roller has a curved outline, 
of which the construction is easy. Thus suppose we want the 
section which will give a slider five complete harmonic swings 
in one revolution of the roller. Make the angle A O B (fig. 2) 
equal to one fifth of four right angles ; describe the circular 
arc AB with O as centre and radius OA equal to R+7, 
where R isthe radius of each of the three circular parts of the 
roller H, J, K, and r the radius of the small friction-wheel on 
the end of the sliding piece; make BD equal to half the 
maximum swing we wish the slider to receive. Then with 
centre B and radius B D describe the semicircle 159, which 
divide into any number of equal parts (eight in the figure), and 
let fall perpendiculars 22, 33, 44, &c. from the points of sub- 
division on to the diameter D B 9, meeting it in the numbered 
points. With O as centre, describe a circular are through 
each of these numbered points in DB. Divide the angle 
A OB into twice the number of equal parts into which the 


semicircle 159 was divided. Then draw a curve 1 C D through 


the intersections of the first are and first radius, the second 
arc and second radius, &e. Finally, draw a great many equal 
circies with radius 7, the centres being in the curve ; then the 
envelope DEF (fig. 3) is one fifth of the whole curved sec- 


tion we wish the curved roller to possess ; and a template of 


tin may be made to be used in the construction of the roller. 


It will be found advisable to construct four templates for each 
division of the roller, since, although a section of the har- 
monic surface described by the centre of the little friction- 
wheel formed by a plane passing through the axis of the large 
roller in a straight line, such a section of the actual surface on 
which the little wheel rests will be curved in consequence of 
y, its radius, not being infinitely small. Our large roller was 
made of hard wood; but it would have been much better if it 
had been made of cast iron or steel, since when of wood it, as 
well as the little friction-wheel of the sliders, must be made 
large to avoid abrasion; but even when these are large it is 


a ee 


of Colour and Visible Motion. 123. 


very difficult to avoid abrasion, and consequent slight irregu- 
larities in the motions of the slider, since the springs pressing 
down these sliders must be moderately strong to cause them 
to promptly follow all the alterations in curvature of the dif- 
ferent parts of the roller. 

Vig. 5 shows (reduced to a scale of one sixth) the roller 
as it came from the lathe before being cut to fit the tem- 
plates ; and figs. 6, 7, 8, 9, 10, 11 the sections at AB, CD, 
HF, GH, IJ, KL (fig. 5) one quarter full size. Small 
circles have been drawn representing the little friction- 
wheel, and at such distances apart that in all cases the time 
taken for the wheel to pass from one position to the next is 
constant and equal to the forty-eighth part of the period of the 
revolution of the roller. 

We used six sliders, «, 8, y, e, €, » (fig. 1), one of which is 
shown enlarged in fig. 4. Hach of these sliders could be 
moved longitudinally, parallel to the axis of the roller, along 
two stout iron bars LM, OP (fig. 1), in order to alter the 
amplitude of the swings. Sliders « and e could be made to 
rest anywhere between B and F, 6 and ¢ anywhere between 
F and G, and y and 7 anywhere between G and C. Each 
slider carried at its upper end a large pulley made to move 
very easily (fig. 4); and the three pulleys of a, 8, y were 
always in the plane of the fixed pulleys T, U, V attached 
above to the wooden frame. A fine inextensible cord passing 
round the movable pulleys «, 8, y, and the fixed pulleys, 8, T, 
U, V, was fixed at one extremity to the pulley V (the pur- 
pose of which was simply to adjust the length of the cord); 
and at the other end, where it hung vertically, it was attached 
to the top of the glass plate abcd, from the bottom of which 
hung a weight in a pail of water to damp the motion of the 
weight. This system then gave to the glass plate the sum of 
the motions of the sliders «, 8, andy. A similar cord over 
e, & mand W, X,Y, Z, together with the cord passing over 
the fixed pulley Q, and to which also hangs a weight in a pail 
of water, gives to the glass plate a horizontal motion equal to 
the sum of the harmonic motions of the sliders ¢, 7. It is 
evident, therefore, that to a circular patch stuck on the centre 
of the glass we were able to give motions compounded of the 


_ above -harmonic motions perpendicular to one another, and 


by projection, by means of an electric light or heliostat, to 
cause this motion to appear like that of a large black ball 
rolling about on a white or coloured background. 

Hyen still greater variety could have been imparted to the 
figures by the metal rods LM, OP (on which the sliders 
moved) having a motion at right angles to the radius of the 
roller. This could easily be arranged if the ends of the metal 


124. Professors Perry and Ayrton on the Music 


rods moved in circular grooves ; and the result would be that 
not only could we alter the amplitude of any one of the com- 
ponent harmonic vibrations by moving a slider along the 
rod, but we could also alter the phase by giving the rod a cir- 
cular motion. ‘To do this, however, satisfactorily would have 
required either the employment of a much larger roller, so that 
the slowest vibration of a slider occurred four or five times 
during one revolution of the roller, or else a change in the 
arrangement. In the illustration (fig. 1) the glass plate, for 
simplicity is shown merely kept in position by the four cords ; 
but in reality it moved in a horizontal frame which again slid 
in a vertical one, so that any lateral motion at right angie: to 
the plane of the glass was impossible. 

The reason why there is necessarily a consider he dis- 
tance between the sets of fixed and moved pulleys is in order 
that a longitudinal motion of the slider shall not alter the mean 
horizontal or vertical position of the spot on the glass. At 
first we had the cords much longer than shown in the figure ; 
but then, even after great care had been taken in endeavouring 
to obtain inextensible cords, some stretching was found to take 
place in practice; consequently we were compelled to deter- 
mine experimentally what was the greatest length of cord that 
could be used without. the stretching interfering with the ac- 
curacy of the motion ; and this length was the one employed 
in the actual apparatus. 

The ingenious way in which a number of pulleys are made 
to give the sum of their motions to the extremity of a cord 
was suggested to us by the arrangement employed in Sir W. 
Thomson’s tide-calculating machine; but it is possible that in 
our new machine we shall adopta totally different plan, and one 
which we think isnew. If the two extremities of a long rigid 
rod have parallel motions perpendicular to the rod, the middle 
of the rod has a motion equal to half the sum of the extremi- 
ties. Thus the parallel motions of two, four, or 2” points may 
be compounded. Similarly for the three points, one third of 
the sum of parallel motions is obtaimed from the centre of a 
rigid triangular piece of which the points are the corners; so 
that by bars and frames of simple construction it is easy to 
get the sum of the parallel motions of any number of pieces. 

We think the roller-plane has much to recommend it; but 
a series of little cranks may be better. Let a number of par- 
allel shafts, having their bearings near their ends on two sides 
of a trough-shaped metal frame, receive from a system of 
spur-wheels near their centres relative velocities 1, 2, 3 
&c. Let A (fig. 13) be either end of any shaft, B being the 
corresponding bearing ; and let there be attached to it, and 


: 
: 


of Colour and Visible Motion. 125 


therefore revolving with it, a sort of double wheel of metal of 
the form shown. I1 isthe pulley round which the cord passes, 
if it is by means of a cord that we sum the harmonic motions ; 
or the pulley may be absent; and the axle of the pulley is then 
simply a crank-pin. Then the rate of revolution of the shaft 
A determines the period, the distance of the axle F G from the 
shaft the amplitude, and the position of F G relative to a fixed 
diameter K L the epoch of the component harmonic motion. 
By shifting, then, the axle F G we may alter the epoch for 
- for the greater amplitudes, and of = for the 
smaller. As there is, however, only a limited change of epoch, 
we think, on the whole, that our improved roller method is to 
be preferred. 

We have used combinations of pure harmonic motions for 

obvious reasons ; but it is possible that, instead of each section 
of the roller giving a pure harmonic motion, it may be found 
more suitable to have it giving some other kind of periodic 
motion ; and such an instrument will differ from the preceding 
in pretty much the same way that one musical instrument 
differs from another. As various means have already been 
devised, by revolving sheets of parti-coloured glass, for pro- 
ducing the effects of the chromotropes of the magic lantern, 
which physiologists have informed us produce such marked 
and instantaneous effects on the nervous constitution, and phy- 
sical organs, of children, we have not yet specially turned 
our attention to the mechanical details of the colour portion 
of our machine. 
_ In what has preceded we have spoken only of projecting the 
motion of a single ball on a wall; but there is no reason why 
the motions of several balls should not be gazed at simulta- 
neously, nor why the people of a large city should not have 
an exhibition of the colour and motion art upon a canopy of 
clouds on a dark night. 


any multiple of 


For assistance rendered us during the construction of this 
apparatus, and for the general intelligent interpretation of our 
wishes, we have to thank our late assistant, Mr. Kawaguchi, 
one of the brightest of the students of the Imperial College 
of Hngineering, and one whose constant earnestness of pur- 
pose, while it rendered his life the more valuable to the scien- 
tific development of Japan, now makes his recent death the 
more to be deplored. 


Phil. Mag. 8. 5. Vol. 7. No. 41. Feb. 1879. L 


fr 126 | 


XVIII. On Catalysis, and the Nomenclature of Oxides. By 
Tuomas Bay ey, Assoc. R.C.Sc.I., Demonstrator of Prac- 
tical Chemistry, Analysis, and Assaying in the Mining School, 

| Bristol*. ; 

year the most remarkable, and at first sight the most 

inexplicable, of the heterogeneous class of reactions 
known as catalyses are the decompositions undergone by hy- 
drogen peroxide in contact with certain substances. But on 
further examination these phenomena afford us the means of 
explaining and differentiating a considerable number of similar, 
reactions and of effecting a classification of them. As is 
well known, hydrogen peroxide, although one of the least 
stable of well-defined compounds when in the concentrated 
form, becomes when diluted, especially in the presence of acids, 
much less subject to decomposition. 

A solution of peroxide of hydrogen, sufficiently dilute to 
remain unaffected for a considerable time when mixed with 
dilute solution of sodic hydrate, may be used effectively in the 
preparation of the peroxides of several metals. If to a solu- 
tion of a cobalt salt, sodic hydrate and then hydrogen peroxide 
be added in the cold, the hydrate of cobalt at first precipitated 
becomes rapidly blackened, and a hydrated peroxide of vari- 
able composition is produced. Almost-immediately a rapid 
evolution of oxygen takes place; and before long the whole of 
the excess of peroxide of hydrogen is decomposed, the cobalt 
peroxide, however, remaining unchanged. Under similar cir- 
eumstances salts of lead and manganese give the same reac- 
tion, namely the formation of a dark-coloured peroxide and 
the decomposition of the excess of hydrogen peroxide. With 
copper the effects are somewhat different: on the addition of 
the hydroxyl the suspended blue hydrate of copper assumes a 
transient yellowish-red colour, but almost immediately resumes 
its original appearance, while the evolution of oxygen proceeds 
as in the former cases. Nickel, although possessing properties 
remarkably resembling those of cobalt, under the influence of 
the mixture of soda and hydroxy] is not peroxidized ; the sus- 
pended green hydrate is permanent, and the liquid retains for 
a long time the properties of a solution of hydrogen peroxide. 
But although the latter has not the power of peroxidizing 
nickel salts, the hydrated peroxide of nickel, formed by other 
means, effects almost as readily as does the corresponding 
cobalt compound the destruction of hydroxyl. It is this dif- 
ference between the behaviour of nickel and cobalt that affords: 
the key to these remarkable phenomena. It is evident, and it 


* Communicated by the Author. 


On Catalysis, and the Nomenclature of Oxides. 127 


is proved by experiment, that a small quantity of cobalt per- 
oxide can effect the decomposition of an unlimited amount of 
hydroxyl, time being, of course, an important factor. On the 
other hand, the amount of hydroxyl destroyed by the nickel 
compound is simply that required for its own decomposition. 

The causes of the resolution of hydrogen peroxide into water 
and oxygen by contact with these peroxides may be due, not 
to any opposite polarity of the two oxygen atoms, contained 
one in the metallic oxide and the other in the hydroxyl, which 
coalesce to yield a molecule of oxygen, but simply to the pre- 
sence of a strain in the two reacting molecules. ‘These oaides, 
water and cobalt or nickel oxide, are compounds in which the 
attractions are, as it were, evenly balanced, the attraction of 
the metal, or hydrogen, being satisfied by the counteracting 
atom of oxygen ; and the fact that special means, such as the 
employment of powerful oxidizers, must be taken to introduce 
additional oxygen into the molecule, justifies the view that the 
latter is held there by a comparatively weak affinity—and that 
the condition of this extra oxygen is such, that when in the 
presence of a foreign body similarly constituted, for example 
hydroxyl, there results an effective outward strain. The affi- 
nity between the extra atoms of oxygen in the two compounds 
being greatest, they coalesce to form oxygen, leaving the me- 
tallic oxide and water. Cobalt, however, has a greater affinity 
for oxygen than has nickel; and while the cobalt oxide thus 
formed becomes immediately reoxidized by the excess of hy- 
droxyl, nickel once reduced is not further acted upon. This 
difference in the deportment of the two metals confirms the 
view that catalysis is due to a series of molecular decomposi- 
tions and reformations of the catalyzing body. y} 

The mutual decomposition of hydroxyl and silver oxide 
closely resembles that between nickel peroxide and the same 
body. For although the silver compound is not a peroxide in 
the ordinary sense, the ease with which it is reduced by heat 
and by comparatively weak reducing agents shows that its 
oxygen is beld by a weak attraction; and when it is in con- 
tact with hydroxyl, there is a tendency for the oxygen in the 
silver oxide and the second loosely combined oxygen atom in 
the hydroxyl to unite. The metallic silver thus produced is 
not reoxidized; and the action is therefore not continuous. 
When hydroxyl acts upon suspended copper hydrate, the first 
product is a yellowish-red substance, probably a peroxide, of 
transient existence, which disappears as soon as the catalysis 
commences, and is never afterwards visible. The action, 
although differing from that of cobalt in that there is no final 
production of a peroxide, resembles it in the essential fact of 


L 2 


— 


128 On Catalysis, and the Nomenclature of Oxides. 


consisting of a series of decompositions and reformations. It 
is therefore a catalysis. Hydrated sesquioxide of iron and hy- 
drate of zinc have no action upon dilute hydrogen peroxide. 
We may therefore argue from this, as from its other proper- 
ties, that sesquioxide of iron is not a peroxide in the sense in 
which the term is used in this paper, namely as denoting an 
oxide in which one or more of the atoms of oxygen are held 
in such a way as to have an outward strain in presence of 
hydroxyl or a similar body. This definition being accepted, 
the sesquioxide of iron must be regarded as the oaide of iron, 
the term protoxide being reserved for the lower compound. 
In the same way we should speak of Ni; O; as a peromide of 
nickel, of NiO as the oxide, and of some lower, at present un- 
known, compound as the protoxide. Our view of catalysis 
being as above stated, it is easy to explain the action of nickel 
or cobalt upon hypochlorites. These are capable of peroxidi- 
zing nickel; and this constitutes the difference between the 
action of the latter with them and with hydroxyl. The cycle 
of operations can be performed and catalysis established. A 
further explanation of the difference between the action of 
copper and of cobalt with hydroxy] suggests itself. The change 
constituting the cycle in the case of copper is from hydrated 
oxide to an unknown peroxide and back again; and since the 
final moment of catalysis, that in which the last hydroxyl dis- 
appears, must consist in the reduction of the copper to the 
lower of the two limits between which the action alternates, 
we find oxide of copper and water as the final products. In 
the catalysis of hypochlorites by cobalt, the two limits are pro- 
_ bably tricobaltic pentoxide (Co; O;) on one side, and cobaltic 

dioxide (CcG2) on the other ; since (Co; O;) has been shown to 
be the result of the reaction. 

The decompositions of dilute hydroxy] are very distinct from 
those which occur to the concentrated compound on contact 
with finely divided silver, gold, or platinum, with various 
oxides (as, for instance, with nickel oxide), and with many other 
bodies. We cannot suppose that finely divided gold or platinum 
is acted upon by hydroxyl; the action is probably connected 
with some power possessed by the surface, and especially by 
edges and by fine particles, of these metals to attract oxygen. 
In concentrated hydroxyl at ordinary temperatures the oxygen 
is quivering on the verge of liberation, and such a surface 
action is sufficient to induce decomposition. 

The phenomena of catalysis thus group themselves into 
physical and chemical. Physical catalyses are those in which 
the catalyzing body, often an inert substance chemically, 
remains unchanged and exerts a surface action purely phy- 


Crystallography of the Nitrosoterpenes of Dr. Tilden. 129 


sical. Chemical catalyses are those which consist of a true 
chemical action; and are distinct from ordinary chemical 
actions only in this, that one of the bodies remains in the 
same state after the action as it was before it. 

According to this view of catalysis and of the constitution 
of oxides, we retain the old terms protowxide, oxide, and per- 
oaide (distinct from acid anhydride) with somewhat different 
meanings. Oxide of copper (CuQ) is no longer the protoxide 
but the oxide ; the unknown yellow body is the hydrated per- 
oxide, while Cu, O is the protoxide. In like manner the oxygen 
atoms which in peroxides are held with the least affinity may 
be called the peroxygen atoms, and those which are the last 
to leave the compound may be called the protoxygen atoms. 
This nomenclature is distinct from the ordinary one founded 
upon the use of the suffixes “ic”’ and “ ous,”’ and of nume- 
rical prefixes, and need in no way interfere with it. Being 
founded strictly upon the chemical behaviour of the compounds 
and not upon the constitution of their molecules, it pos- 
sesses evident advantages ; but the other terms have important 
uses, and might with advantage be retained in the majority of 
instances. 


_ XIX. Crystallography of the Nitrosoterpenes of Dr. Tilden. 
By N.S. Masxetynyu, /.2.S.* . 
[Plate VII. figs. 1-6. ] 

HE varieties of nitrosoterpenes obtained in crystals by 
Dr. Tilden belong to two crystalline types. The first 
includes the substances formed (a) from ordinary turpentine, 
(6) from French turpentine, (c) from juniper turpentine. 
To the second type belong the substances obtained from the 

oils of orange, of bergamot, and of caraway. 

I. First group.—The crystals of nitrosoterpene produced in 
different ways from the American oil of turpentine have 
already been described in connexion with Dr. Tilden’s notice 
of the substances in the Journal of the Chemical Society, 
June 1875. They were of two kinds, differing in habit—the 
one being twinned on the plane 001, and the other not evin- 
cing any twin habit. The crystals obtained from French oil of 
turpentine and from juniper oil are very dissimilar in appear- 
ance to those made from the American oil; but a goniome- 
trical study of them proves that they belong to the same crys- 
talline type with those previously investigated. The crystals 
of the latter kinds furnished me by Dr. Tilden presented con- 
siderable difficulty under measurement, since certain of the 
faces are rounded ; and from their. being very minute and in- 

* Communicated by the Crystallological Society. 


130 | Prof, N.S, Maskelyne on the Crystallography 


clined at small normal angles on each other, it is often difficult 
to discriminate the faces lying in a particular zone, as the 


greater number of the determinations have to be made with — 


faces which offer no images or such as are very confused, and 
which can be measured only by the method of maximum illu- 
mination. 

The figures 1 and 2 represent the same forms as those 
already given in the Journal of the Chemical Society. Fig. 3 
exhibits the forms which exist on the crystals obtained from the 
French and the juniper oils, together with some other forms, 
of which the existence on some of the crystals is probable, 
though no reliable measurements could be obtained from them. 
The crystals rapidly lose by exposure such lustre as they have 
when fresh—apparently in consequence of evaporation taking 
place at ordinary temperatures, as evinced by a faint odour 
perceptible even while a little crystal is exposed on the go- 
niometer. 

The measurements obtained from crystals of the different 
sorts are arranged incolumns,—the first column consisting of the 
calculated angles as given in the earlier communication to the 
Chemical Society ; column II. containing the angles obtained 
by measurement of the crystals thus described, which were 
obtained from American and ordinary oil of turpentine. Co- 
lumns ITT. and LV. give the averages of the angles (omitting the 
extremes) as obtained by measurements from the crystals made 


from French and from juniper turpentines respectively ; while 


column V. gives the angles calculated on average data, obtained 
from what seemed to be the better measurements, yielded by the 
two latter varieties of the crystal. The forms on these “ French”’ 
and “‘juniper’’ nitrosoterpenes were by no means uniformly 
the same. Some of the crystals were very complicated, ex- 
hibiting numerous forms of which even the zone-positions 
could be only approximately ascertained; others were much 
simpler, the faces of the forms {111}, {201}, {110}, in one 
case 031 apparently, with traces of 001, forming the combi- 
nation. On others the form uw or {3 12! seemed the most im- 
portant face. The faces of the form {110} are in the latter 
varieties always corrugated by a series of planes inclined at 
from 1° to 3° on each other, approximately in the zone 
[110,001]. The following letters represent the faces and 
forms of the crystals:— | 


a, {100}; m, (110); ,{010}5; m’,(110); m’,(110); : 
k, {101}; 6, {201}; ¢, f0013; A, s011t; m 0aure 
p, {Ll lt; 4, 4112}; ¥,{332}3 uw, 18 12) p, toma 
r, {851}. 


# 
: 
: 
: 


ee em 


mc)m' 
ap 


_.of the Nitrosoterpenes of Dr. Tilden. 


eoesee 


eesses 


@erses 


eeeres 


eaesesn 


II. 


Ame- 
rican. 


eaeeee 


erase 
e@srece 
eeveoe 
eeesee 
e@ersee 


@eeree 


@oseee 


eeeeee 


TILE. 
French. 


eeteoee 
B@eeses 
eeostee 


eeneee 


75° 7’ to 39! 
approx. 


eeeeee 


131 approx. 


@evenr 


about 28° 


IV. 


Juniper, 


75° to 75° 
105 18 


19’ 


101 472 


about 68° 35’ 
64 30 


87 22 
67° 30’ to 70° 


28° 40’ approx. 


eesezeseae 


Vv: 
Calculation. 


131. 


A facile cleavage runs parallel to the face (001); a less 
facile cleavage is parallel to the faces of the form {110}. 
The great facility with which the former cleavage is produced 
precluded the forming sections for the polariscope. 

In one crystal which showed one of the ring-systems the 
plane of the optic axes was evidently perpendicular to the 
plane of symmetry, the acute bisector lying in that plane; and 
it appeared that the dispersion of the bisectors in that plane 
for different colours gave the position of the bisector for blue. 
rays nearer to the normal of a, or (100), than that of the red 


132 Crystallography of the Nitrosoterpenes of Dr. Tilden. 


rays. The position of the acute bisectors was approximately 
determined as being about 114° on the normal to (100), and 
321° on the normal to (101). : 

II. Second group.—tThe second type of the crystals of nitroso- 
terpene (figs. 4 & 5) includes those formed from the oils of 
orange, bergamot, and caraway. They belong to the mono-sym- 
metric system ; and their arc-elements may be represented as 
100 001=79°1',100 101=38° 2532’,100 110=40°25Y. 
The crystals representing the orange and the bergamot pre- 
parations, especially the former, generally give fairly good 
images from the faces 001,101, and 110; those from 
100 are usually in the condition of many bands; while the 
reflections are never good from the face 101. The faces {001} 
are generally hollowed. ‘The reflections from the faces on the 
caraway crystals, and particularly from 100, are less perfect 
than those from the other preparations. In the following 
Table the measurements marked with an S were made by Mr. 
Hlliot Steel. The only faces that occur on any of these crys- 
tals are those of the following forms :— 


a, {10033 ¢, {O01}; &, {101}; d, {101}; m, {110} 


Calculated. Bergamot. Orange. - Caraway. 

te) i 5e) i ° ° ‘ ° 4 
ae 7a 1 9° 224998. +179 79 
ak Sot Be Pe ceszans 37 14 ~—_—_s88 to 40° 
cad 24 44 | 24 4(|24° 6S. | 24 4&24 63/24 8 
da' 76 543 | 77 2|76 348. | 76 56 Ol 
ad 103 54 | 103 33 103 5 | 
mm 599 99 47/199 108. ¢ 1.99: 9 | Bae 
m mm! 80 51 80 52 Sol cous 80 52. 
am 40 254 | 40 263 | 40258, | 40 26-27' = (40 21 | 40°30'S. 
m ke 53 234 | 
m d 99 56 99 58 to 

100 2 99°50' 

mC 81 394 | 81 41 | $1 888. 81° to 52° 


A distinct cleavage runs parallel to the faces of the form 
001. It was not possible to determine the direction in the 
crystal of the acute bisector of the optic axes. 


III. Terpene Hydrate (fig. 6). 


Crystals of terpene hydrate, made by Dr. Tilden from dextro- 
and from levo-rotatory turpentine-oil, exhibit no distinction 
in the character of their forms. They are in fact crystallo- 
graphically identical, belonging to the orthosymmetrical (or 
rhombic) system, and presenting the forms a {100}, m{110}, 
o {111}, and £{101}, and occasionally 5 {0 1 0}. 


: 


On an Artificial Diopside Rock. 133 


- The crystals of terpene hydrate have been measured by List 
(Pogg. Ann. vol. lxvii. p. 364), by Rammelsberg (Crystallogr. 
Chem. p. 406, and Suppl. p. 227), and by Arzruni, who has 
also determined the optical characters of the substance. The 
measurements made by me accord very nearly with those ob- 
tained by Arzruni. 
The parameters of the crystal are 
a:b: c=0°8082: 1: 0°4788, 

the angles calculated from which elements, and the averages 
of those obtained by measurement on four crystals (two from 
each source), form the two columns in the following Table:— 


Angles. By calculation. Arzruni. By measurement. 
am = 51 3 30 : : Bhot gee” 
mn = 7 53 77 49 20 17 538 
eed &3h 3805630 38 564 
ee == UB 96 30 64 262 
oe = 5° 8 51 18 
moe == 252: 44 52 49 40 52 36 15 
bo i = (67 37 30 67 374 
arene == [4445 44 38 30 44 49 

bo == hb D4. 

oes =) 28 6 28 1 30 28 

meee a Gy Ee 56 8 30 56 2 30 


The faces m give in general excellent images ; the faces 0 give 
a banded image. Arzruni’s parameters are 0°80722 :1:0°47640. 


XX. Onan Artificial Diopside Rock formed in a Bessemer Con- 
verter by Mr. Percy Gilchrist. By N. 8. Masxetynz, F.R.S.* 


R. MASKELYNE drew the notice of the Society to the 
production of diopside ona considerable scale at Bleen- 
avon by Mr. Percy Gilchrist and Mr. Sidney Thomas, during 
some experiments those gentlemen conducted having in view 
the elimination of phosphorus in the Bessemer converter. The 
artificial diopside was produced in a downdraught kiln at a 
yery intense and prolonged heat—the kiln being lined with 
silica bricks, which were in contact with a moderately alumi- 
nous and siliceous magnesian limestone. The product result- 
ing from the action of the bricks on the limestone occurs 
in large masses, portions of which present the appearance of 
an interlaced mass of glistening crystals of a grey hue. 
Here and there, in hollows, minute crystals are met with 


* Communicated by the Crystallological Society. 


134 On an Artificial Diopside Rock, 


presenting faces; and on placing one of these on the gonio- 
meter the nature of the mineral was placed beyond doubt. 

It is,in short, diopside, with the forms m, {110}; b, {010}; 
o, {221}; s, {111}, asis seen from the following comparison 
of the calculated with the measured angles :— 


Calculation. Found. 

mm == 8t B 87.18 45 
|mb = 43 324 43 36 
Lab == 46275 46 21 
[m'o = 35 25 35 3894 
Kin = 98 46 59 38 
-ms = 78 56 78 44 


Two specimens of this artificial rock were analyzed by Mr. 

Gilchrist, and gave the numbers in columns 1 and 2:— 
(1) (2) (3) (4) 
MeOh sa. 7. ibs 1°63 1°38 
ANS Og 3s 2 2d 2°47 | 
CaO> = . 2 1900 21-00 25°09 25°93 
Niet ts). on 14°45 16°49 17°36 18°52 
HBr... ©. CBO 58°75 56°03 ay) 
101°05 = 100°34 99°82 100-00 

These analyses correspond very nearly to that of a diopside 
containing one equivalent each of calcium and magnesium ; 
but with an admixture of silica in the one case of about 17, 
and in the latter case of 14°5 per cent. in excess. 

This ingredient is doubtless a mechanical adjunct to the 
diopside, and is derived from the silica brick, to the presence 
of which the formation of the diopside is due. The portions 
of the mass in which the alkaline earths are in excess do not 
contain the diopside, and they gradually become slaked on 
exposure to the air. The composition of such an ideal diop- 
side would be that indicated by the numbers in column (4), its 
formula being (Ca} Mg) 8103. 

Column (3) represents the results of an analysis by Rammels- 
berg of a diopside from Retzbanya, which is given for compa- 
rison with that of the artificial diopside rock. The artificial 
production of an augitic mineral is no new fact; but the for- 
mation on a considerable scale of a veritable diopside rock 
appears to be as novel as it is interesting. 


P18% 2} - 


XXI. Enstatite Rock From South Africa, 
By N.S. Masxetyne, £.2.S.* 


R. MASKELYNE exhibited sections of a rock trom two 
d different localities in the Transvaal, which, when exa- 
mined under the microscope, presented all the characters of a 
very crystalline enstatite without affording evidence of the ad- 
mixture of other minerals ; and this anticipation of its nature has 
been subsequently confirmed by Dr. Prevost in Mr. Maske- 
lyne’s laboratory at Oxford. ‘The specimens from which the 
sections were made were collected by Mr. Dunn, who described 
the two rocks in question as forming hills of boss-like form at 
Korn Kopje, and at a place twelve miles south of Holfontein in 
the Witfontein Mountains, to the south of Lydenburg in the 
Transvaal, 

The occurrence of a pure and massive énstatite rock is new 
to petrology, though rocks.(such as lherzolite) are known in 
which enstatite is a very prominent ingredient mineral. Its 
occurrence in South Africa has, moreover, a special interest, 
since Mr. Maskelyne first asserted the enstatitic or bronzitic 
origin of the rock in which the diamonds occur in that region 
of the world. The serpentinized mass of which the diamond- 
mines are composed was first shown, on crystallographic and 
microscopic grounds, to have contained, and in no inconsider- 
able degree to have consisted of, bronzite (ferro-magnesian 
enstatite); and this was confirmed by actual analysis, by Dr. 
Flight, of the grains of bronzite still left unaltered in that 
rock. (See Quart. Journ. Geol. Soc. vol. xxx. p. 406, 1874.) 


The diamantiferous rock, however, contains other minerals, 


and must have been not very dissimilar to lherzolite. The en- ~ 


statite rock from the neighbourhood of Lydenburg is, on the 
other hand, composed nearly exclusively of that mineral, which 
is chiefly familiar to the mineralogist from its being an im- 
portant ingredient of meteorites, and is likely,in other respects, 
to become recognized as a more frequent ingredient of rocks 
than has hitherto been anticipated, though, like the kindred 
mineral olivine, the more ferruginous kinds have frequently 
undergone a more or less complete serpentinization. The 
Baste rock in the Hartz and the so-called pseudophite of Zdjar 
are known to be still rich in enstatitic mineral, though other- 
wise almost completely metamorphosed ; and in many serpen- 
tines, suchas that of the Lizard, crystals whole or in part still 
survive as witnesses to the original nature of the rock. Mr. 
'T, Davies has also pointed out to the author of this notice that 
the eulysite from Tunaberg presents, under the microscope, 
the characteristic features of enstatite or bronzite in one of its 


* Communicated by the Crystallological Society. 


136 M. V. von Lang on a Horizontal Goniometer. 


ingredient minerals—the other minerals associated with it 
being olivine and garnet, as is the case in some specimens of 
lherzolite, though the two rocks are quite dissimilar in aspect. 

The following Table exhibits the analysis (1) of the Korn- 
Kopje rock by Dr. Prevost, in which all the iron is assumed to 
be in the ferrous condition ; (2) of a rock from the Radauthal 
(occurring in bastite) in the Hartz, by Streng (Jahrb. Min. 
1862); (3) of that in the lherzolite of L. Lherz, by Damour 
(Bul. Géol. xxix. p. 413) :— 


() (2) (3) 
UCR ak ae we foe 5415 54°76 
POMONA, So we eee BO 3°04. 4°90 
Ferrous oxide . Set ORL 9°35 
Manganous oxide. . 2 
Maonesia . i. 2 2 ee or 28°37 30°22 
Lime. cae gigs Lge PANT | 

98°97 100°10 99-23 


The excess of lime in the analysis is probably traceable to 
an augitic mineral, a diopside, probably present as an ingre- 
dient, although not yet recognized by the microscope in the 
sections made from the South-African rocks. In fact the mi- 
croscope, so invaluable as an instrument for pioneering in the 
realm of petrology, is frequently an untrustworthy guide when 
too much relied on—that is to say, when the results obtained 
by it are not checked and confirmed, and in fact supplemented 
by the more tedious methods of investigation pursued in the 
laboratory. 


XXII. On a Horizontal Goniometer. By Victor von Lane*. 
[Plate VII. figs. 7 & 8.] 


i pe instrument represented in fig. 8 owes its existence 

to the necessity of being able to measure refractive 
indices at different angles of incidence. This is of great im- 
portance when one wants, like Professor Stokes, to verify the 
theoretical formule of double refraction by experiment, or 
when one tries, on the contrary, to determine with the aid of 
these formule the constants of double refraction from obser- 
vations on a prism of arbitrary position. 

The measurements I made in order to determine the figure 
of the wave-surface in quartz near its axis belong to the first 
kind of researches ; whereas the determination of the refrac- 
tive indices of gypsum I have just finished gives an example 
of the second kind of researches, as for that determination one 
single prism was made use of, 

* Communicated by the Crystallological Society. 


} 
| 


M. V. von Lang on a Horizontal Goniometer. 137 


The chief requisites of such an instrument are two concentric 
axes—the inner one carrying the vernier and the prism-table, 
the outer movement carrying the telescope and the graduated 
circle. A collimator with slit is, of course, fixed to the tripod 
of the instrument. 

The two axes are not put into one another, as is done in 
geodetical instruments, for the sake of repeating the angles ; 
but here the tripod (G) is terminated in a strong cone that 
forms the axis on which the circle (C) turns, whereas a hole 
in the centre of the cone supports the axis (A) of the vernier 
(n). Fig. 7 shows this arrangement in asectional drawing. 

Both axes may be clamped by the screws L L’, and micro- 
metrically moved by the screws MM’. Suppose we clamp 
the inner axis with the prism, of which the angles of deviation 
(D) and of incidence (7) are to be measured. Let 8 be the 
reading of the vernier by direct observation of the slit, R the 
reading by observation of the slit after reflection from the 
first plane of the prism, and T the reading by observation of 
the spectrum. Then we have 

D=T—S, 1=90°—4(S—R); 
and the index of refraction in the direction given by the angle 
y is found from the known formule 

7 — tan (* — 5) = tan tan i— | ieee 
A being the angle of the prism. 

As long as the relative position of the prism and the vernier 
is not altered, we have 

S+R=C= constant. 
For if we turn the prism (with the vernier of course) through 
an angle +y, all readings will increase in the same ratio; but 
the reflected image of the slit turns at the same time through 
an angle —2y, so that the sum S+ 8 will indeed remain con- 
stant. We find by the quantity C, 


1=90°+ . —S8; 


and this formula allows us to find the angle i from the read- 
ing 8. In this way it is possible to determine the angle of 
incidence even when it is very small; in which case it cannot 
be observed directly, as telescope and collimator cannot be 
brought so near to each other. 

_ If we put the telescope to the slit and then turn the inner 


axis till the vernier gives 90°+ = then the light will fall per- 


138 - Messrs. Wanklyn and Cooper on the 


pendicularly on the first plane of the prism, the angle 7 being 
then evidently zero. | eam 2 

Of course the angle of the prism can also be determined 
with this instrument; and itis not necessary to alter any thing 
in its arrangement or to move the prism. . We have only to 
clamp the telescope in a position of about 90° to the collimator, 
and then to observe the reflected image alternately on both 
faces of the prism. 

In order to be able to use the instrument for other pur- 
poses, both telescope and collimator can be shifted parallel to 
their axes and be fixed by the screws OO’. If the instru- 
ment is to be used as a spectroscope, one may put conveniently 
before the objectives of telescope and collimator prisms with 
direct vision. 


XXIII. The Moist-Combustion Process: some Reactions of Al- 
kaline Permanganate of Potash. By J. ALFRED WANKLYN 
and W. J. CooPER*. | 


pA DS up our investigations (the results of which 
were communicated in the June Number of this Journal, 
and in the Chemical Section of the British Association at the 
Dublin Meeting last year), we have now to announce that we 
have overcome one of the difficulties which stood in the way 
of giving to our process absolute generality of application to 
all organic substances. 

It will be remembered that, starting with the organic sub- 
stance in aqueous solution, we showed that permanganate of 
potash and excess of alkali burnt down the organic substance 
to the state of carbonates, oxalates, and water; and we pro- 
posed to render the solution acid, and so, as was well known, 
would burn down the oxalates to carbonates. At the Dublin | 
Meeting we announced that although this answers very well 
In many cases, yet in certain classes of cases acetates ap- 
peared among the products of oxidation; and when once pro- 
duced, acetates resisted further oxidation. 

We have now managed to oxidize the acetates, by the 
simple process of using considerable excess of permanganate 
and raising the temperature some 60 or 80 degrees above the 
boiling-point of water. Under these conditions acetate of pot- 
ash yields carbonate of potash, and apparently no oxalate what- 
ever. 

There is a difficulty, however, attendant on the use of these 


* Communicated by the Authors. 


Moist-Combustion Process. 139 


high temperatures; and on this occasion we wish to explain 
this difficulty and how it has been overcome. 

The difficulty arises from the fact that, at temperatures very. 
little above 100° C., a mixture of pure permanganate of potash 
and caustic potash evolves oxygen gas. This fact we have 
very carefully ascertained, both by noting the diminution in 
oxidizing-power which the solution shows after being heated 
to 180° in the oil-bath, and hy actually collecting and mea- 
suring the oxygen gas which was evolved during the heating 
in the oil-bath. The gas is evolved very freely at tempera- 
tures even below 140° C.; and the numerical results accord 
very fairly with this equation :— 


Here, as will be observed, the permanganate of potash is re- 
presented as losing one fifth of its active oxygen, and yielding’ 
manganate of potash. 

It has long been known that at very elevated temperatures, 
at temperatures bordering on low redness, permanganate of 
potash parts with oxygen and forms manganate of potash— 
that, in point of fact, at these elevated temperatures manga- 
nate, and not permanganate, is the stable form of combina- 
tion ; but we believe this easy evolution of oxygen at tempe- 
ratures a little above the boiling-point of water is quite a 
novelty. For the moist-combustion process it would be a very 
uncomfortable novelty if we were unable to stop the evolution 
of the gas by a convenient device, since the alkaline perman- 
ganate would cease to keep a trustworthy record of the con- 
sumption of oxygen during the process. 

We have, however, to add that we can stop the evolution 
in a most convenient manner. _We mix some hydrated bin- 
oxide of manganese with the permanganate and alkali; and 
then there is no evolution of oxygen. Why this addition 
should be effective is obvious ; and the chemist will have no 
difficulty in understanding that the necessity of having to 
make such a condition does not damage our process. 

We have to record, as an interesting reaction, the behaviour 
of green oxide of chromium with strongly alkaline solution of 
permanganate of potash. It acts very readily, and yields 
chromate of potash and hydrated binoxide of manganese ; this 
takes place at temperatures even below the boiling-point of 
water. We are following up this experiment, and hope to 
make new and rare metallic acids. : 


fr 440°] 
XXIV. Notices respecting New Books. 


The Speaking Telephone, Talking Phonograph, and other Novelties. 


By Grorce B. Prescorr. Fully Illustrated. New York: D. 
Appleton and Company. 1878. (8vo, pp. 431.) 


pHs volume is divided into thirteen chapters, of which the first 

nine contain an account of the Speaking Telephone, the tenth 
is devoted to the Talking Phonograph, and the last three to the 
“‘ other novelties,” viz. Quadruple Telegraph, Electric Call Bells, 
and the Electric Light. The subjects comprised in this list are at 


present matters of general interest ; and a book which gives a good 


deal of information respecting them will doubtless obtain a large 
number of readers. The printing and general appearance of the 
book are much in its favour. The illustrations, which are nume- 
rous, are well execu‘ed, and will help the reader to form a distinct 
conception of the objects they represent. 

It will be observed that the largest part of the volume is devoted 
to the telephone. The reason of this we may state in the author’s 
words :—‘ The question as to whom we are indebted for the tele- 


phone is one which, in consequence of the conflicting statements 


that have appeared from time to time, is, to say the least, extremely 
puzzling. We have, therefore, endeavoured to give it the attention 
its importance demands, in order to arrive at a true solution of the 
problem, and, in doing so, have taken every opportunity to consult 


all available authorities on the subject. No effort has been spared 


in our investigation to obtain all the facts as they are; and these 
are now given as we have found them, without favour or prejudice ” 
(p.i). Mr. Prescott’s grammar is not quite perfect ; but his mean- 
ing is sufficiently plain; and, it comes to this, that he has written 
his book for the purpose of advocating the claims of Mr. Gray to 
be considered the inventor of the Telephone. This appears very 
clearly in the first chapter, which gives a general description of the 
instrument in its principal forms. After an account of Reiss’s 
Musical Telephone, which transmits the pitch but not the variations 
in the intensity and other qualities of the ‘tone, the author describes 
the principles on which three Telephones are constructed. All 
three agree in the main point that vibrations caused by the voice 
of the sender are made to transmit electric waves of varying inten- 
sity through a circuit, and these reproduce the vibrations at another 
point and thereby transmit the sounds to the receiver with all their 
variations of pitch, intensity, and quality. In Gray’s telephone 
this is effected by causing the current to pass through a fluid from 
one wire to another wire, which moves with the membrane put into 
vibration by the voice, and thus the fluid space traversed varies with 
the amplitudes of the vibrations and subjects the current to a vary- 


ing resistance. In Bell’s telephone the membrane carries a light 


permanent magnet placed near the poles of an electromagnet; the 
vibrations of the membrane therefore induce a succession of mag- 
neto-electric pulsations varying in intensity with their amplitudes, 


4 


Notices respecting New Books. 14] 


and causing corresponding variations in the intensity of an electro- 
magnet placed at another point of the circuit, where these varia- 


_ tions produce vibrations precisely resembling the original vibrations. 


In Dolbear’s telephone the electromagnets are replaced by perma- 
nent magnets surrounded by helices : the receiving and transmitting 
diaphragms are precisely alike, and, in place of a membrane, consist 
of small disks of thin iron plate. The vibrations of the one plate 
induce magneto-electric currents, which vary the force of the mag- 
net at the other end of the circuit and thereby produce correspond-~ 
ing vibrations in the other plate. The peculiarity of this form of 
the instrument is that its action is reciprocal; either end may be 
the receiver, and the other the transmitter. The chapter also con- 
tains an account of several of the improved forms of the Telephone ; 
but with these we are not concerned. The main point consists in 
the dates assigned to these three inventions; and these dates, we 
may observe, are by no means stated with due distinctness. Our 
author tells us that Mr. Elisha Gray, of Chicago, invented his me- 
thod subsequently to the spring of 1874 (pp. 14, 15); that Pro- 
fessor A. G. Bell, of the Boston University, exhibited his instru- 
ment, in the summer of 1876, at the Centennial Exhibition in 
Philadelphia (p. 16); and that Professor A. EH. Dolbear, of Tufts 


_ College, made his improvements in the ensuing autumn (p. 19). 


This is, perhaps, a suflicient statement of Mr. Prescott’s case. In 
the following chapters he allows the several claimants to speak for 
themselves :—Chapter 11. contains Professor Beil’s account of his 
researches, in a lecture delivered to the Society of Telegraphic 
Engineers; chapter v. Mr. Gray’s account of his experimental 
researches ; and chapter viii. an abstract of ‘“‘ Researches in Tele- 
phony,” by Professor A. EH. Dolbear. 

The above statement suggests one or two remarks :—First. It 
does not seem clear from chapter viii. that Mr. Dolbear claims 
priority of invention; but if he does, the claim does not appear to rest 
on documentary evidence. Secondly. In chapter v. we fail to find 
any confirmation of the date apparently given on page 14 for Mr. 
Gray’s invention, which we have very briefly described above, viz. 
the spring of 1874*. We do, indeed, find a very surprising coinci- 
dence, viz. “‘a verbatim copy” of Gray’s specification and of Bell’s 
specification, both filed in the United-States Patent Office on the 
same day, viz. Feb. 14, 1876. In the former of these documents 
Mr. Gray says, “I claim as my invention the art of transmitting 
vocal sounds or conversations telegraphically through an electric 
circuit” (p. 205); while in the latter Mr. Bell claims, inter alia, 


“the method of, and apparatus for, transmitting vocal or other 


* Strictly speaking, Mr. Prescott says that in the spring of 1874 Mr, 
Gray ‘invented a method of electrical transmission by means of which 
the intensity of tones, as well as their pitch, was properly reproduced at 
the receiving station” (p. 14), and that subsequently he invented the Te- 
lephone above described. “Subsequently” may, of course, mean any 
thing. We think, however, that the suggestion of the passage (pp. 14, 15) 
is as above stated. In chap. v. there is no trace of the Telephone until a 


few weeks before the date of the specification, viz. Feb. 14, 1876. 


Phil, Mag. 8, 5. Vol. 7. No. 41. Feb, 1879. M 


142 Geological Society. 


sounds telegraphieally as herein described” (p. 215). Thirdly. It 
must be borne in mind that Mr. Prescott distinctly advocates Mr. 
Gray’s claim. This, indeed, is clear from what has been already 
said; andif further confirmation were needed, it would be found, for 
example, i in the notes on p. 71 and p. 73, and in the passage at the 
end of chapter v. on p. 217: he by no means keeps to the attitude 
of a candid inquirer, which he appears to assume in his preface. 
On this side of the Atlantic we shall be very much surprised if Mr. 
Bell’s claims to priority of invention are successfully contested ; 
still the matter is one which must be adjudicated in the United 
States. 

Of the remaining parts of the volume there is not much to say. 
They seem to us by no means well drawn up. From time to time 
the composition is very slovenly. In the contents there are both 
excess and defect. or instance, in the chapter on the Electrie 
Light a good deal is said which the reader might be presumed te 
‘know, while the parts relating to “novelties” are eut very short. 
In several cases elaborate figures are given marked with half the 
letters of the alphabet, and plainly designed to accompany detailed 
explanations ; the explanations, however, are not there (figs. 202, 
203, and 207 are instances). Another very serious fault—and the 
more serious as the book deals in part with evidence —is the way im 
which documents are quoted and extracts made from other writers. 
It is never easy, and sometimes impossible to tell whether an ex- 
tract is given verbatim, and even where it begins and where it ends. 
Still, with all its faults, the book is one of considerable interest, and 
will doubtless find many readers. 


XXV. Proceedings of Learned Societies. 


GEOLOGICAL SOCIETY. 
[Continued from p. 67.] 


Jan. 8, 1879. —Henry Clifton Sorby, Esq., F.R.S., President, in the 
Chair. 


a following communications were read :— 

1. “On some Tin-deposits of the Malayan Peninsula.” B 
Patrick Doyle, Esq., C.K. (Communicated by the Rey. T. Wiltshire, 
ME Acs a AUS, eG.) 

The tin-ore of the Malayan peninsula is obtained from “ stream- 
works” in an alluvial plain extending between a range of granitic 
mountains and the sea. The author describes the mines of the 
district of Larut Perak. The ore is got in open workings at an 
average depth of about 10 feet. The tin-bearing stratum has an 
average thickness of 4:87 feet; it is overlain by stratified sand and 
clay, and rests upon either porcelain-clay or, sometimes, a sandstone. 
The ore varies from a fine sand, near the sea, to a coarse gravel, 
near the mountains, and is mixed with quartz, felspar, mica, and 
schorl. The author is of opinion that the stratum of ore has been 
derived from the granite of the mountain-range (in which it still 
occurs in veins) by denudation, and under conditions which still 
exist, though in a modified form, 


Intelligence and Miscellaneous Articles. 143 


2. “ Description of Fragmentary Indications of a huge kind of 
Theriodont Reptile (Titanosuchus ferox, Owen), from Beaufort West, 
Gough Tract, Cape of Good Hope.” By Prof. R. Owen, C.B., F.B.S., 


3. “ Notes on the Consolidated Beach at Pernambuco.” By J.C. 
Hawkshaw, Hsq., M.A., F.G.S. 

The consolidated beach at Pernambuco, which has already at- 
tracted considerable notice, is a ridge of sandstone from 25 to 75 
yards wide, and, as shown by borings made under the author's 
direction, from 10 to 13 feet thick. The landward or higher edge 
is nearly at the spring-tide high-water level; and it slopes seaward, 
the river (with a depth of 28 feet at low water 60 feet from the 
rock) flowing aleng the former face. The rise and fall of spring 
tides is 7 feet. Beneath the above rock is a stratum of sand with 
shells and stones about 8 feet thick, and then a second layer of 
sandstone rock. 

The consolidated beach is cemented by carbonate of ime, which 
the author considers to have been deposited by the action of water 
percolating through the rock, probably when the level of the land 


differed somewhat from what it is at present. He thinks it possible 


that this and other similar beaches on the Brazilian coast may mark 
periods of répese in the slow vertical movements which the coast has 
undergone. 


XXVI. Intelligence and Miscellaneous Articles. 


> NOTE ON ELECTROMAGNETS IN TELEGRAPHY. 
BY OLIVER HEAVISIDE. 

N a recent Number of this Journal I stated :—‘ On telephonic 
circuits the reduction in current-strength is nearly inversely 
proportional to the pitch of the sound,” &c. This is only true for 
a constant electromotive force. Thus it would be correct for a 
battery telephone. The strength of very rapid currents from a 
battery through an electromagnet is nearly inversely proportional 
to the rapidity. Butinan electromagnetic telephone, although the 
electromotive impulse produced by a semivibration of the iron disk 
of the sending telephone is constant for all pitches, provided the am- 
plitude of the vibration is the same, yet when the semivibration is 
executed in half the time, the mean value of the electromotive force 
is doubled. Thus, instead of the second partial tone of a conti- 
nuous sound being weakened nearly twice as much as the first, it 
will not be quite so much weakened. TI being the current, R the 


resistance, L the electromagnetic capacity, and m= a where T is 
the time of a complete vibration, then T 
as mE 
VJ R?+ Lim 
in the case of a Bell telephone, where E is proportional to the am- 
plitude of vibration of the sending disk. Keeping E constant, Tr 


increases slightly with m. Also, when R is increased, I is reduced 
more for low pitches than for high. 


144 Intelligence and Miscellaneous Articles. 


ON TWO NEW FLUORESCENT SUBSTANCES. BY E. LOMMEL. 
From Dr. Th. Schuchardt, of Gorlitz, I received, some time since, 


two new fluorescent substances, the examination of which (by the 


method L have previously described) gave the following results. 

_ 1. Anthracene-Blue-—The deep-blue etheric solution fluoresces 
intensely olive-green. The absorption-spectrum shows four dark 
bands, the darkest parts of which are situated at 36, 55,.69, and 


86, respectively, of Bunsen’s scale, and a darkening of the violet 


end, commencing a little before H, while the blue and the greater 
part of the violet appear almost unaffected. Of the absorption- 
bands the second and the third (55 and 69) are by far the most 
intense and about equal in intensity ; then follows, in the order 
of intensity, the rather feeble first (86); and last comes the still 
feebler fourth (86). The spectrum of the light of fluorescence 
begins faint at 27, distinct at 30, and extends distinct as far 
as 70, faint as far as 74. It shows three maxima, at 40, 52, 
and 63, separated by two very clearly marked minima (at 45 
and 57), and hence appears to consist of three bright bands— 
one red, one orange-yellow, and one green-yellow—of which the 
middle one a little exceeds the others in brightness. The fluo- 
rescence-spectrum projected upon the liquid commences faintly at 
47, and shows two very bright fluorescence-bands corresponding to 
the two most intense absorption-bands, divided by a tolerably dark 
interspace, and strongly distinguished from one another by their 
different colouring; namely, the first is entirely orange-coloured, 
the second yellow-green. A third, but much fainter, brownish 
olive-green-coloured maximum at 86 corresponds to the fourth 
absorption-band ; the first, on the contrary, has no part in the 
fluorescence. In the blue and the violet, from F to shortly before 
Hi, the fluorescence is very slight, olive-green to reddish, and 
scarcely perceptible ; only just before H does it again become more 
intense, and extends with an olive-greenish tone into the ultra- 
violet. We have here, therefore, a fluorescing substance, with 
which the blue and the greater part of the violet rays exert only an 
extraordinarily feeble, while the orange-yellow and yellow-green rays 
exert a very intense excitant action. If we excite with homogeneous 
light, descending gradually to continually less refrangibility, we 
observe that the entire fluorescence-spectrum is excited by all the 
rays down to 58—by the ray 58, for example, not merely the por- 
tion from 30 to 58, but also the more refrangible from 58 to 70. 
The rays below 58, however, do not excite the yellow-green part 
of the light of fluorescence (58 to 70), but only the red and orange- 
coloured part, but this also entirely: for example, if we excite with 
the ray 48, the fluorescence-spectrum from 30 to 55 is distinctly 
seen; light which has passed through three red glasses, and only 
reaches to 50, excites still very distinctly up to 57. Accordingly 
the fluorescence-spectrum of anthracene-blue consists of two parts, 
separated by the minimum at 57, neither of which obeys Stokes’s 
rule, and the second, more refrangible, is excited only by the rays 
above 57. Anthracene-blue therefore behaves like a mixture of 


Intelligence and Miscellaneous Articles. 145 


two fluorescent substances of the first class*, one of them charac- . 
terized by the absorption-band 55 and orange-yellow fluorescence 
(30 to 57), the other by the absorption-band 69 and yellow-green 
fluorescence (57 to 70). 

2. Bisulphobichloranthracenous Acid.—The faintly brownish- 
yellow-coloured etheric solution presents no absorption-bands, but 
only a slight absorption of the blue and a stronger of the violet rays. 
Tt fluoresces at its surfaces a very beautiful blue, from its interior 
greenish. The spectrum of its fiuorescence-light extends from 30 
to 162, (therefore to the violet end), and shows four maxima—viz. 
between 70 and 80, at 109, 131, and 150, of which the first three 
appear about equally intense, the last somewhat less so. Between 
these maxima are feebly marked minima to be perceived at about 
98, 117, and 140. The fluorescent spectrum commences (faintly) 
at about F, and extends, with an olive-greenish tone of colour and 
slight intensity of light, up to abont 150, here almost suddenly be- 
comes a beautiful blue and very bright, attains its greatest bright- 
ness, immediately before H, and reaches, with the same blue colour, 
far into the ultra-violet. The fluorescence is of the second kind, 
2. é. follows Stokes’s rule-—Wiedemann’s Annalen, 1879, No. 1, 
pp- 115-118. 


ON THERMAL RADIATION AT HIGH TEMPERATURES. 
BY J. L. SORET. 

In some researches the results of which I have previously made 
publict, I arrived at the conclusion that Dulong and Petit’s law of 
thermal radiation ceases to be found true at very high temperatures. 
Since then I have made, according to other methods, a few similar 
experiments, which I have not yet published, because I wished to 
complete and render them more exact. Long ago I spoke of them 
to M. Raoul Pictet, who, now engaged in a critical investigation on 
solar heat, has asked me for some information on the subject; and 
this has induced me to give the following compendious summary of 
those experiments, imperfect as they are. 

When an electric current is caused to pass through a conducting 
wire, the temperature of the wire rises until the heat which it loses 
by radiation, by contact with the air, and by conductivity at the 
points of attachment becomes equal to the heat evolved in its inte- 
rior by the electricity. We can, on the one Land, estimate this last 
quantity of heat, and, on the other, by estimating the temperature 
taken by the wire, calculate the quantity of heat which it ought to 
emit according to the law of Dulong and Petit. 

* Compare Wied. Amn. iii. p. 125 (1878). 

+ In accordance with the theory (see Wied. Ann. iii. p. 251, 1878), 
each of these two parts of the fluorescence-spectrum would represent the 
emission-spectrum belonging to the corresponding absorption-bands dis- 
placed somewhat downwards, or each of the two absorption-bands would 
ah to be regarded as the “reversal” of the fluorescence-band belonging 

o it. 

{ Archives des Sciences Phys. et Naturelles, 1872, t. xliv. p. 220, t. xlv. 
p. 252; 1875, t. hii. p. 89&c.; 1876, t. lv. p. 217. Phil. Mag. [IV.] vol. 1 
p. 155 (1875). 


146 Intelligence and Miscellaneous Articles. 


Seeking to make some comparisons of this sort, I have employed — 


the dynamoelectrical machine of the Geneva University, which was 


set to work by first passing the current through a Serrin lamp, or 


any other equivalent resistance, until the machine had acquired its 
normal velocity. Then, by means of a commutator, the current 
was directed through a platinum wire, while the lamp was excluded 
from the circuit. The wire grew rapidly hot, and soon melted. 


The dynamoelectric machine is driven by an hydraulic motor of - 


nominal four-horse power. All this force is far from being em- 
pleyed; but let us suppose that itis. A four-horse power corre- 
sponds to a work of 18000 kilogrammetres per minute, equivalent 


to 42°3 calories. Suppose, further, that the dynamoelectric ma- ~ 


chine is perfect, and that all the motive work is converted into 
electric current; neglect the heat evolved in the machine itself and 
in the conductors that convey the current to the platinum wire, 


upon which we will suppose that the whole effect is concentrated. 


That wire will therefore receive, as a maximum, 42°3 calories (a 
number which in reality is certainly four times too much). 

The diameter of the platmum wire was 0°31 millim.; therefore 
its cylindrical surface was 1 square millim. per millim. of current. 


The length of the wire, in three experiments, was 385 millims. It. 


was melted in a few seconds, and broke at several points. On after- 
wards examining its fragments, traces of liquefaction were every- 
where recognized. We may therefore conclude that the whole of it 
was raised to the temperature of fusion of platinum, which, accord- 
ing to the lowest estimates, exceeds 1700°. The total surface of 
the radiation was 385 square millims.; but let us reckon only 3 
square centims., in order to make a liberal allowance for the cir- 
cumstance that the two extremities may be cooled a little by con- 
tact with the electrodes; and, finally, let us neglect the loss of heat 
by contact with the air. Upon these data let us calculate the quan- 
tity of heat emitted by this wire according to the law of Dulong 
and Petit, taking the formula given by Pouillet, 


e=9fa!,— 
where ¢ is the quantity of heat, one gram of water heated 1° being 


taken as unit; g a constant, of which the value is 1:146 when the | 


square centimetre is taken for the unit of surface, and the minute 


for the unit of time; 7 is the emissive power; a is the constant of 


Dulong and Petit, or 10077; ¢ the temperature. We will adopt 
the number given for the emissive power by MM. La Provostaye 
and Desains, f=0-°092. 

On making the calculation, putting t= 1700, we find 48541 units 
of heat, or 48°541 calories, per square centimetre of radiating sur- 
face. For the whole of the wire, then, 145-623 calories should 
have been evolved if the law of Dulong and Petit were applicable, 
while the motor could supply only 42°3 at the most. The differ- 
ence is enormous. 

Another method, capable of giving much more exact if not more 
striking results, consists in taking a pile,atangent-compass, and com- 
pleting the circuit by a platinum wire of a certain diameter and a 


Saad 


Intelligence and Miscellaneous Articles. 147 


eertain length, which becomes heated to a temperature which can 
be estimated in different ways. The deflection of the compass is 
observed when it has become stationary. The wire is then replaced 
by a thinner one, of which the length is varied until the compass 


gives the same deflection as before; the rest of the circuit remains 


unchanged. The resistance of the stout and long and that of the 
short and thin wire are evidently equal, and the quantities of heat 
evolved in their interiors are the same. 

Operating thus with two platinum wires taken from the same 
sample, one of them 0-62 millim. in diameter and 538-7 millims. in 
length, and the other of 0°31 millim. diameter and 77-7 millims. 
length, the same deflection was obtained. The ratio of the two ra- 
diation-surfaces is therefore 

2x 538°7 
(eat 
The radiation per unit of surface of the thin wire was therefore 14 
times as much as that of the thick wire (neglecting the heat taken 
away by contact of the air). - 

On the other hand, the thick wire was raised to a temperature 
much below red heat (it did not char wood), while the thin wire 
became white-hot. If we admit that the difference of temperature 


— ee 


was only 600° (a figure certainly too low), the heat emitted per 


unit of surface by the two wires should have been, according to the 
law of Dulong and Petit, in the ratio of 1 to 100, and not 1 to 14 
as was given by the experiment”*. 

JI made some more trials by a very different method. A globule 
of platinum, as large as possible, placed in a magnesia cupel, is 
fused by the flame of a little blowpipe with illuminating-gas and 
oxygen well mixed. The heat evolved by the gas in burning is 
about 5600 calories. per cubic metre; therefore, if the pipe con- 
sumes 1 litre per minute, neglecting the losses (which are necessa- 
rily considerable), the maximum of heat that can be communicated 
to the platinum is 5:6 calories. Then, if we estimate the radiating 
free surface of the metallic globule, which is raised to the tempera- 
ture of fusion of platinum at least, we can calculate the quantity of 


* M. Kd. Becquerel also arrived at similar results, although to my 


' knowledge he has not discussed them from the point of view occupied by 


us. He operated upon a platinum wire placed im vacuo and passed through 
by an electric current of varying intensity; and he calculated the heat 
evolved internally by multiplying the square of the intensity of the cur- 
rent by the resistance of the wire, measured at each experiment. Passing 
thus from a temperature much below red heat to one near the melting- 
point of platinum, those quantities of heat did not change in the ratio of 
1 to 18.-- La Lumiere, t.1. p. 92. 

We may also cite Professor Tyndall's experiments, who, on measuring 
with a thermoelectric pile the intensity of a single kind of obscure radia- 
tions, found that the energy of the radiation of a platinum wire changes 
in the ratio of 6 to 122 in passing from a temperature below red heat to 
that of an intensely white heat. According to the law of Dulong and 
‘Petit, the ratio ought to have been as 6 to 600, supposing that the differ- 
ence between these two temperatures amounted to only 600°.—Za Chaleur, 
trad. frang. p. 414. 


148 Intelligence and Miscellaneous Articles. 


heat that ought to have been emitted according to the law of Dulong 
and Petit. It is found to be much more than 5-6 calories — 
Bibliotheque Universelle, Archives des Sciences Physiques et Naturelles, 
Jan. 15, 1879, t. i. pp. 86-90. 


ON ELECTROCHEMICAL ACTIONS UNDER PRESSURE. 
BY A. BOUVET. 


In a series of about fifty experiments, each lasting several hours, 
and during which I have been able to produce with extreme facility 
pressures of 100, 200, 300 atmospheres, &c., I constantly recog- 
nized the existence of the two following laws :— 

(1) The decomposition of water by a current is independent of 
the pressure ; 

(2) The quantity of electricity necessary for decomposing one 
and the same weight of water is sensibly the same, whatever may 
be the pressure at which the decomposition is effected. 

I have ascertained by experiment that the mechanical theory of 
heat perfectly accounts for these two laws. Thus, by taking ad- 
vantage of the fact that gases produced in the midst of water are 
obtained at a sensibly fixed temperature, I verified the formula 
which represents the work expended for the compression of gases 
without change of temperature :— 


T— =v (@ = PV log hyp =. 


T, work =V,, final volume after the expansion ; 

V, volume of the compressed gas ; 

P, pressure. 

The result of the experiment made with gases at 200 atmospheres 
agreed perfectly with the result calculated after the above formula. 

For the sake of brevity, I will only add the following :— 

Ist. The oxygen and hydrogen, at whatever pressure, are libe- 
rated with equal facility. 

2nd. These two gases may be produced in a single test-tube or 
in two; in neither case are there any secondary phenomena deter- 
mining even partial recombination, as has hitherto been believed. 
The precise and constant indications of the manometer, the regular 
increments, of pressure, ascertained from minute to minute during 
several consecutive hours, leave no doubt on this point. 

3rd. The oxygen and hydrogen, when they are collected in one 
and the same test-tube, even under considerable pressure, and 
although constituting the explosive mixture, are not at all dan- 
gerous. 

The electrodes I employed were of platinum. I always took care 
_to let them be completely immersed. 

In the course of my experiments, lasting several months, I never 
ascertained any appreciable variation of temperature, although I 
sometimes employed currents possessing very energetic tension.— 
Comptes Rendus de lV Académie des Sciences, Dec. 30, 1878, tome 
Ixxxvil. p. 1068-69. 


i 


a a 


ce  —————EEE— ES 


| THE 
LONDON, EDINBURGH, anv DUBLIN 
PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES. | 


MARCH 1879. 


XXVIII. Acoustical Observations. II. 
By Lorp Rayirieu, /.2.S.* 


Pure Tones from Sounding Flames. 


a best approximation to a pure tone is doubtless that 

given by a fork held over a suitably tuned air reso- 
nator; but unless the vibrations are maintained, the sound is 
of but short duration, and varies in intensity throughout. On 
the other hand the introduction of an electro-magnetic main- 
tenance (as in Helmholtz’s vowel experiments) somewhat 
complicates the apparatus. For many purposes extreme 
purity and constancy of pitch are not important; and thus an 
arrangement which shall be simple and easy to manage, even 
though less perfect in its operation than a tuning fork, is still 
a desideratum. 

During the last year I have often used with good effect air 
resonators whose vibrations were maintained in a well-known 
manner by hydrogen-flames. In the common form of the ex- 
periment an open cylindrical tube is employed as resonator, 
and gives a sound, usually of a highly compound character. 
In order to obtain a pure tone, it is only necessary to replace 
the tube by a resonator of different form, such as a rather wide- 
mouthed bottle or jar; but a difficulty then arises from the 
progressive deterioration of the limited quantity of air in- 
cluded. A better result is obtained from a tube with a cen- 
tral expansion, such as a bulbous paraffin-lamp chimney, 
which allows of a through draught, and yet departs sufficiently 


* Communicated by the Author. 
Phil. Mag. 8. 5. Vol. 7. No. 42. March 1879. - N 


150  — Lord Rayleigh’s Acoustical Observations. 


from the cylindrical form to give a pure tone. For ready 
speech, it is sometimes necessary to restrict the lower aperture, 
e.g. by a bored disk of wood attached with wax. Another 
plan which answers very well is to block the middle of a cy- 
lindrical tube by a loosely fitting plug. The tubes that I used 
are of cast iron, and were plugged by rectangular pieces of 
wood provided with springs of brass wire to keep them in 
position. The length of the plug may be about two diameters 
of the tube ; the length of the tube itself should be about 
twelve diameters. In all cases the best result requires that 
the tubes through which the hydrogen is supplied be of suitable 
length, and be provided with suitable burners. These may 
be made of glass, and are easily adjusted by trial. 

For ordinary purposes a common hydrogen-bottle is suffi- 
cient ; but the note is rather more steady when the hydrogen 
is supplied from a gas-holder. In this way I have obtained 
pure tones, giving with tuning forks pretty steady beats of 
more than two seconds’ period. When the intensities are 
nearly equal, the phase of approximate silence is very well 
marked. 


Points of silence near awall from which a pure tone is reflected. 


On this subject there are two papers by N. Savart *, who 
advances views very difficult of acceptance. A criticism of 
some of Savart’s positions was published soon after by Seebeck; 
but the question does not appear to have been thoroughly 
cleared up. 

One source of confusion is imperfect recognition of the 
fact that the positions of the silences depend upon the nature 
of the apparatus used for the investigation. In the case of 
the ear a silence requires that there be no variation of pres- 
sure at the open end of the ear-passage, whether it be in its 
natural state, or prolonged by a tube fitted into the external 
ear. The addition of a small cone or resonator will not affect 
the truth of this statement. Thus, if the influence of the head 
and body of the observer acting as simple obstacles be put out 
of account (as may fairly be done when a tube is used), the 
silences occur at distances from the wall which are odd mul- 
tiples of the quarter wave-lengthf. On the other hand, if a 
membrane simply stretched over a hoop and held parallel to 
the wall be used as the indicator, the positions of zero dis- 
turbance are at distances from the wall equal to even multiples 
of the quarter wave-length. 

In the theory of organ-pipes the places of zero velocity 


* Ann. d. Chim. 1xxi. 1839, x1. 1845. 
+ The waves are here supposed. complete, Savart’s “ oniliege are only 
half as long. 


Lord Rayleigh’s Acoustical Observations. 151 


and of maximum pressure-yariation are usually called nodes; 
and the places of zero pressure-variation and of maximum 
velocity are called loops. If we retain this nomenclature, we 
may say that silences as investigated by the ear occur at 
loops, and that the maximum sound is found at nodes; but in 
Savart’s papers the silences are identified with nodes. More- 
over the difference is not one of words merely; for Savart con- 
siders that (apart from the effects of obstacles) the silences 
are to be found at distances from the wall which are even 
multiples of the quarter wave-length. A large part of his” 
work is thus an endeavour to bring the facts into accordance 
with a mistaken theoretical view. 

When the median plane is parallel to the wall, the obstruction 
presented by the head displaces considerably the positions of 
the silences. In his first paper Savart proposes to add 27 
mm. to the measured distances between the external ear 
nearer to the wall and the wall itself, in order to take account 
of the interval between the external ear and the sentient ap- 
paratus. - In the case of the ear further from the wall a similar | 
distance is to be subtracted. J am ata loss to understand how 
the situation of the sentient apparatus can be supposed to be an 
element in the question at all. Hvery thing must surely de- 
pend upon whether there is or is not a variation of pressure at 
the outer end of the ear-passage. In the second paper Sa- 
vart takes (as it appears to me) a further step in the wrong 
direction. He states that the positions of the silences are the 
same, whether they be observed with the ear nearer to the 
wall, or with the ear further from it, and draws the conclusion 
that the part of the head with which we have to deal is that 
situated in the median plane midway between the ears. Having 
already added 27 mm. to his measurements (in the case of the 
ear nearer to the wall), to take account of the distance between 
the external ear and the labyrinth, he now adds 50 mm. 
more. Jy this artificial treatment the distances of the silences 
from the wall are made to agree with the series of even multi- 
ples of the quarter wave-length, though considerable anoma- 
lies remain unexplained. 

There can be no doubt, I imagine, that Savart’s theoretical 
views are quite erroneous, and that what has to be explained 
by the action of the head as an obstacle is the displacement of 
the silences from the loops, and not from the nodes. An exact 
theoretical investigation of this subject is of course out of the 
question ; but some information bearing upon it may be ob- 
tained from a calculation given in my ‘Theory of Sound,’ 
§ 328, relating to the character of the obstruction to sound pre- 
sented by rigid spheres. It are that if a source of sound 

2 


152 Lord Rayleigh’s ichistient Observations. 


be situated at the surface of a sphere whose circumference 
is moderate in comparison with the wave-length, the phase 
(which is the element on which the phenomena under con- 
sideration principally depend) at a distance is approximately 
the same as if the source were moved outward from the surface 
through a distance equal to half the radius, and the sphere 
were removed altogether. By the theorem of reciprocity, 
§ 294, it follows that in the case of reflection of plane waves 
there is a silence at the point on the surface of the sphere 
nearest the wall when, not this point itself, but another fur- 
ther from the centre by half the radius, is distant from the 
wall by an odd multiple of the quarter wave-length, provided 
that the distance between the sphere and wall be not too small 
a multiple of the radius. Instead therefore of adding with 
Savart 27 mm., or 77 mm., to the observed distances in the 
expectation of so arriving ‘at even multiples of the quarter 
wave-length, we ought rather to subtract some such distance 
as 50 mm. in the expectation of arriving at odd multiples of 
_ the same quantity. 

The following are some of Savart’s results given in the 


first paper :— 
Designations des divers Distances des points 
points. a la parol. 

metres. 

Paroi. 0-000 

1" ventre. "148 

1* noeud. 373 

2° ventre. “716 

2° neeud. 1:000 

3° ventre. 1°:358 

3° neeud. 1°615 

4° ventre. 1:997 

A° noeud. 2275 


If we subtract 27+50 (=77) from Savart’s numbers for 
nodes we get 
296, "923, 1:538, 2°198, 


eorresponding to E 
3619), §(619,) (619), §(619), 


"309, SAT 1°546, - 2163 5 
619 deing the value of the half-wave (onde The “ ventre ”’ 
between the wall and the first node does not belong to the 
regular system at all. 
From a theoretical point of view, it appeared to me highly 
improbable that the silences for the two ears should occur in 
the same position of the head, except perhaps in the case of a 


or to 


ee ee 


! 


Lord Rayleigh’s Acoustical Observations. 1538 


particular wave-length equal to about three diameters; and 
laboratory experiments with steadily maintained tones had 
made me familiar with the phenomenon of sounds apparently 
transferring themselves from one ear to the other when the 
head is moved ; but I thought it desirable to try a few experi- 
ments in the open air especially directed to the examination of 
this point. | 

The source of sound was a lamp-chimney and hydrogen- 
flame, as described above, of pitch é' flat, so that the quarter 


wave-length was about eleven inches. The apparatus was 


placed at distances varying from about 18 to 50 feet in front 


_ ofa tolerably flat wall; and the observer, with one ear stopped, 


investigated the positions of the silences, holding the middle 
plane of his head parallel to the wall. Although the positions 
of the silences were not very well defined, presumably in con- 
sequence of unequal amplitudes of the superposed vibrations, 
the most inattentive observer could not fail to notice that 
it was necessary to move the head considerably in order to 
pass from a place where the sound was a minimum for one 
ear to a place where it was a minimum for the other ear. We 
may therefore conclude that Savart’s statement is not generally 
true, and that the views which he has founded upon it have 
no sufficient claim upon our acceptance. 

When the median plane of the head is perpendicular to the 
wall, the silences are observed at distances which are odd multi- 
ples of the quarter wave-length, agreeably with theory. 


Sensitive Flames. 


The beautiful phenomenon of sensitive flames is now 
familiar to students of acoustics; but its rationale is by no 
means understood. An important contribution to the facts, 
from which some day a theory will doubtless arise, is con- 
tained in the observation of Prof. Tyndall as to the “ seat of 
sensitiveness.”’ My present purpose is to bring forward 
another fact which also will probably be found important. It 
may be thus stated. Under the action of stationary sonorous 
waves a flame is excited at loons and not at nodes. 

The source of sound was a little contrivance on the principle 
of the bird-call, blown from a well-regulated bellows. Pro- 
bably a very high organ-pipe or whistle might be employed ; 
but it is necessary to use a nearly pure tone ; and the pitch 
must be high, or the flame will be not affected sufficiently. 
At a distance of a few feet the sound was reflected perpendi- 
cularly from a large board. The flame itself was that called by 
Tyndall the vowel flame, issuing from a pin-hole steatite burner 
fed from a gas-holder with gas at high pressure (9 or 10 inches). 


154 Lord Rayleigh’s Acoustical Observations. 


The observations were made by moving the burner to and fro 
in front of the board, until the positions were found in which the 
flame was least disturbed by the sound; and it will be seen from 
the results that these positions were very well defined. The 
distances between the board and the orifice of the burner was 


then taken with a pair of dividers, and measured on a scale 


of millimetres. Two observers, J and H, adjusted the flame 
independently of one another. The following are the results 
obtained :— | 


Burst pocition |... He tele an ae ee } 163 | 16:25 
Second position...... uP at Ee ? sen 314 157 
Third position ....../4 a ie cee : hee 462 | 156 
Fourth position .../15) gy a cau eee eat t 622° | 156 
Fifth position .....:- Toye ese ee "7g | 78x | IBS 


The second column contains the individual measurements 
by the two observers ; the third shows the mean of all the 
results for the same position. The numbers in the fourth 
column are the results of dividing those of the third column 
by 1, 2, 3, 4, 5, respectively, and agree very well together, 
proving that the positions coincide with nodes. If the 
positions had coincided with loops, the numbers of the third 
column would have been in the ratios 1: 8: 5: 7: 9. The 
wave-length of the sound was thus 31:2 mm., corresponding 
to pitch fF. 

A few observations were made at the same time on the 
positions of the silences, as estimated by the ear listening 
through a tube. As was to be expected, they coincided with 
the loops, bisecting the intervals given by the flame. When 
the flame was in a position of minimum effect, and the free 
end of the tube was held close to the burner at an equal 
distance from the reflecting wall, the sound heard was a 
maximum, and diminished when the end of the tube was 
displaced a little in either direction. It may therefore be 
taken as established that the flame is affected where the ear 
would not be affected, and vice versd. 


Aerial Vibrations of very Low Pitch maintained by Flames. 


In a lecture “On the Explanation of certain Acoustical 
Phenomena,” * I showed the production of a pure tone of 
about 95 vibrations per second from a glass resonator and a 


* Proceedings of the Royal Institution, March 15, 1875. Nature, vol. 
xviii. p. 319, | 


| 
\| 


Lord Rayleigh’s Acoustical Observations. 155 


hydrogen-flame. With a larger resonator of the same kind 
—a globe with a short neck, intended for showing the com- 
bustion of phosphorus in oxygen, the pitch is 64 vibrations 
per second. I have lately made some further experiments, 
with the view of finding whether there is any obstacle to the 
maintenance by flames of vibrations of still lower frequency. 
The resonator, whose natural pitch is 64, was fitted with a 
paste-board tube 2 inches in diameter and 14 inches long. 
In this condition its calculated frequency * is about 25; and 
it was found that vibrations could be maintained by a hydrogen- 
flame, or even by a flame of common gas. The supply-tube 
should be of considerable length ; and the orifice must not be 
much contracted. Although the intensity of vibration was 
such as to make it a matter of difficulty to keep the flame 
alight, scarcely any thing could be heard. I saw no reason to 
doubt that still slower vibrations might be maintained by 
flames. ; 

In illustration of the mechanics of this subject, an apparatus 
was contrived, in which by the aid of electricity a periodic 
communication of heat to a Jimited mass of air could be 
effected. By means of a perforated cork one leg of a U-tube 
containing mercury was fitted air-tight to the neck of an 
inverted bottle of about 200 cub. centims. capacity. The dia- 
meter of the column of mercury was about 1 centim., and 
the leneth of the column about 25 centims. The combina- 
tion constituted a resonator, differing from an ordinary air 
resonator by the substitution of mercury for air in the 
channel joining the interior of the vessel with the external 
atmosphere. Inside the bottle was a spiral of fine platinum 
wire, at one end in communication through the cork with one 
pole of a battery of two or three small Grove cells. The 
other end of the platinum spiral was connected with a copper 
wire, which terminated in the U-tube near the equilibrium- 
position of the mercury-surface. The second pole of the 
battery was in permanent connexion with the outer extremity 
of the mercury column. As the mercury vibrates, the circuit 
is periodically completed and broken. The current passes, 
and the platinum wire glows, when the mercury rises in the 
leg connected with the bottle. Thus the communication of 
heat occurs when the air in the interior is condensed by the 
vibration, which is the necessary condition for maintenance, 
as is explained in the lecture referred to. 


hijke’s Notes on a large scale. 
The production of sound in tubes by heated gauze was 


* ‘Theory of Sound,’ vol. ii. § 307 (8). 


: 
: 
: 


156 Lord Rayleigh’s Acoustical Observations. 


discovered by Rijke*, and is perhaps the most interesting 
of all the cases in which vibrations are maintained by heat. — 
The probable explanation is given in the Royal-Institution 
lecture. It is surprising that the phenomenon is not more 
generally known, as on a large scale the effect is extremely 
striking. JI have employed a cast-iron pipe 5 feet long and 
4 inches in diameter, hung over a table from a beam in the ~ 
the roof of my laboratory. The gauze (iron wire) is of about 
32 meshes to the linear inch, and may advantageously be 
used in two thicknesses. It should be moulded with a hammer 
on a circular wooden block of somewhat smaller diameter than 
that of the pipe, and will then retain its position in the pipe by 
friction. When it is desired to produce the sound, the gauze 
caps are pushed up the pipe to a distance of about a foot, and 
a gas-flame from a large rose-burner is adjusted underneath, 
at such a level as to heat the gauze to a bright red heat. For 
this purpose the vertical tube of the lamp should be prolonged, 
if necessary, by an additional length of brass tubing. In 
making the adjustment a more convenient view of the interior 
of the pipe is obtained with the aid of a small piece of 
looking-glass held obliquely underneath. Sometimes a sound 
is excited by the flame itself independently of the gauze. 
This should be avoided if possible, as it impedes the due heat- 
ing of the gauze. When a good red heat is attained the 
flame is suddenly removed, either by withdrawing the lamp 
or by stopping the supply. of gas. In about a second the 
sound begins, and presently rises to such intensity as to shake 
the room, after which it gradually dies away. The whole 
duration of the sound may be about 10 seconds. 


Mutual Influence of Organ-Pipes nearly in unison. 


The easiest way of approaching the consideration of this 
subject is to take the case of an open or stopped pipe, divided 
into two similar parts by a rigid barrier along its middle plane. 
In the absence of the barrier, the vibrations of the two halves 
under the action of the wind are in the same phase ; and at 
first sight there appears to be no reason why this state of things 
should be disturbed by the barrier, Nevertheless it is well 
known to physicists that the two halves do in fact take opposite 
vibrations, with the result that the sound in the external air 
at a distance from the compound pipe is a small fraction only 
of that due to either half acting alone. In the pipe itself the 
vibration is more, and not less, intense on account of the 
barrier. It is true that at the very beginning of the sound, 


* Pogg. Ann. cyii. 339, 1859, 


- a ee, erm ea a 


Lord Rayleigh’s Acoustical Observations. 157 


when the wind first comes on, the vibrations in the two 
halves are similar, as is evidenced by the greater loudness ; 


_ but the opposition of phase is rapidly established, usually in a 


fraction of a second of time. Asa system with two degrees 
of freedom, the compound pipe is capable of two distinct 
modes of vibration, in one of which the vibrations of the 
component pipes are in the same phase, and in the other in 
opposite phases. Why the action of the wind should maintain 
the latter mode of vibration to the exclusion of the former 
has not hitherto been explained ; but the fact remains that 
that mode of vibration, which depends for its possibility upon 
the barrier, is chosen in preference to the other mode, which 
is not dependent upon the barrier, and in the absence of the 
barrier is the one necessarily adopted. 

The two possible modes of vibration have, as in almost all 
such cases, two distinct periods of vibration, the difference 
depending upon the behaviour of the air just outside the 
open ends. In consequence of the inertia of the external air 
at an open end, the effective length of a pipe exceeds its 
actual length by about six tenths of the radius. The in- 
crement of effective length is therefore greater in the case of 
the compound column of air when its parts vibrate in the 
same phase, than it would be for either of the parts if removed 
from the influence of the other. On the other hand, when 
the vibrations are in opposite phases, the increment must be 
much less, one component pipe absorbing the air discharged 
from the other. Accordingly one note of the compound pipe 
is graver, and the other, which is the one actually sounded, is 
more acute, than the natural notes of the component pipes 
when supposed to act independently of one another. 

In order to show this effect it is not necessary that the two 
pipes be similar, or even of exactly the same pitch. If two 
pipes in approximate unison be placed so that their open ends 
are contiguous, a mutual influence is exerted, which is usually 
sufficient to prevent the production of beats. The examples 
about to be given will show that the unison need not be 
exact ; but the greater the deviation from unison, the more 
intense is the residual sound. Beyond the limit of the ad- 
missible departure from unison, beats ensue; but at first 
they are irregular, and lable to be disturbed by very slight 
causes, such as draughts of air. According to theory, the 
frequency of the beats ought to be a little greater than the 
difference of the frequencies of the notes given by the pipes 
independently ; but I have not been able to detect the difference © 
experimentally. It would therefore seem that over most of 
the range for which the mutual influence is sensible and 


158 Lord Rayleigh’s Acoustical Observations. 


regular, it is sufficiently powerful to prevent more than one 
note being sounded. 

In the experiments that I have tried, the pipes were blown 
from a bellows provided with a special regulator, and the 
pitches of the various notes were determined by counting the 
beats for 20 seconds between them and a somewhat sharper 
note on a harmonium. Sometimes the blown ends of the 
pipes were near together, and sometimes (in the case of open 
pipes) the unblown ends ; but during the course of an experi- 
ment the positions of the pipes were not altered. In order 
to prevent a pipe speaking, I placed some cotton wool over the 
wind-way, and sometimes inserted a stopper; so that the pitch 
of the pipe as a resonator was entirely altered. The following 
are the details of some of the observations :— 

I. Sept. 23. Open metal pipes about 2 feet long, one of 
them provided with an adjustable paper slider for modifying 
the pitch. Blown ends near one another ; unblown ends distant. 


Beats per second with harmonium-note. 
One pipe alone. | Other pipe alone, | Both pipes together. 
AS, 4:5 | 5°0, 4:8 3:2, o5lg 
So that the note given by both pipes together is decidedly 
sharper than those of the separate pipes. » 


II. Sept. 23. Same pipes as in J. Unblown ends near 
one another ; blown ends distant. 


Beats per second with harmonium-note. 

One pipe alone. | Other pipe alone. 
4-8 51 

III. Sept. 25. Same pipes placed parallel to one another 


at a distance of about 14 inches. : 


Both pipes together. 
3°8 : 


Beats per second with harmonium-note. 
One pipe alone. | Other pipe alone. | Both pipes together. 
5°15, 5°20 5°30, 5°45 5°00, 5:15 
The note of both pipes together is somewhat higher than 
the notes of the single pipes. 


IV. Sept. 26. Same pipes. Unblown ends near; blown 
ends distant. 
Beats per second. | 
One pipe alone. | Other pipe alone. | Both pipés together. 
5°80, 5°85) | 715,750, 7°45 | 5°35, 5°50, 5°45 
V. Sept. 26. Two bottles, tuned with water to about g, 
were blown by wind issuing from flattened tubes connected 


Lord Rayleigh’s Acoustical Observations. 159 
with the bellows by lengths of india-rubber tubing. When 


the bottles were sufficiently removed from one another, the 
mutual influence was very small, being insufficient to prevent 
the formation of slow and pretty steady beats of about four 
seconds’ period. This experiment shows that the mutual in- 
fluence depends upon the proximity of the open ends of the 
pipes, and not upon any effects propagated through the supply- 
pipes leading from a common bellows. 

Some further remarks on this subject will be found in a 
paper read before the Musical Association, Dec. 2, 1878. 
Reference may also be made to some allied experiments by 
Gripon*, with which I have only lately become acquainted. 
They appear scarcely to extend to the case with which I have 
principally occupied myself, namely that in which both pipes 
are blown. M. Gripon had, however, anticipated me in the 
experimental determination of the effect of a flange in modi- 
fying the correction for an open end? of a pipe. 


Kettledrums. 


The theory of the vibrations of uniform and uniformly 
stretched flexible circular membranes, vibrating in vacuo, has 
been known for many yearst. In practice deviations from 
such theoretical results are to be expected, if only in con- 
sequence of the reaction of the air, which must operate with 
considerable force on a vibrating body exposing so large a 
surface in proportion to its mass. In the case of kettledrums, 
the problem is further complicated by the action of the shell, 
which limits the motion of the air on one side of the membrane. 

From the fact § that kettledrums are struck, not in the 
centre, but at a point about midway between the centre and 
edge, we may infer that the vibrations which it is desired to 
excite are not of the symmetrical class. I find, indeed, that 
the sound undergoes little, if any, change when the central 
point is touched by the finger. Putting therefore the sym- 
metrical vibrations out of account, we have to consider the 
parts played by vibrations of the following modes :—(1) that 
with one nodal diameter and no nodal circle ; (2) that with two 
nodal diameters and no nodal circle; (3) that with three nodal 
diameters and no nodal circle ; (4) that with one nodal diam- 
eter and one nodal circle, &c. The investigation proved to be 
of greater difficulty than I had expected, partly in consequence 
of the short duration of the sounds. Better ears than mine 

* Ann. d. Chim. iii. p. 371, 1874. 

+ Phil. Mag. June 1877. 

_{ ‘Theory of Sound,’ ch. ix. 
§ De Pontigny. Proceedings of the Musical Association, Feb. 1876. 


160 Lord Rayieigh’s Acoustical Observation: 


are liable to be puzzled in attempting to analyze compound: 
sounds of such complication and irregularity. The following 
results, however, are believed to be trustworthy. 

The principal tone corresponds to mode (1); the tone cor- 
responding to (2) is about a fifth higher ; that of mode (3) 
is about a major seventh above the principal tone ; the tone of 
mode (4) is a little higher again, forming an imperfect oc- 
tave with the principal tone. For the corresponding modes 
of a uniform membrane vibrating in vacuo, the theoretical in- 
tervals are those represented by the ratios 1°34, 1°66, 1°83, or 
about a fourth, a major sixth, and an interval nearly midway 
between a major and a minor seventh, respectively. 

In experimenting on this subject it is important to bear in 
mind that the system of tones is really double, and that its 
components coincide only on the supposition of perfect sym- 
metry. In practice the requirement of symmetry is difficult 
to attain even approximately ; and thus it is that beats are 
generally heard, arising from the superposition of vibrations 
of nearly equal frequency. For the purpose of identifying 
the various modes, the want of symmetry is rather advan- 
tageous than otherwise. In the case of the gravest mode, I 
fastened with cement a small load (a halfpenny) to a point 
of the membrane situated about halfway between its centre 
and edge. In this way the two gravest tones fell asunder to 
about a semitone, one of them (the graver) being excited 
alone by a blow anywhere along the diameter through the 
load, the other alone by a blow anywhere along the perpen- 
dicular diameter. With the aid of a resonator tuned to the 
pitch of the subordinate tone, the nodal diameters of the two 
modes (1) may be fixed with great precision by the absence of 
beats. With a resonator turned to a pitch midway between 
those of the two tones, the beats are most distinct when the 
blow is delivered at a point near the middle of one of the 
four quadrants formed by the two nodal diameters ; but the 
position for the most distinct beats necessary varies with the 
pitch of the resonator, and also with the situation of the ob- 
server. It may be remarked that, provided the deviation from 
symmetry be moderate, the same vibrations (except as to phase) 
are excited, whether a blow be delivered at any point, or at 
the other point on the same diameter equally distant from the 
centre ; and vibrations excited by striking one point are 
damped by touching the other. The other modes with nodal 
diameters only were identified in a similar way. ‘The mode 
(4) with a nodal circle is known by the cessation of sound at 
a particular point when various places along a radius are tried ; 
on either side of this point the sound revives. 

The drum that I examined is of about 25 inches diameter; and 


Lord Rayleigh’s Acoustical Observations. 161 


the form of the shell is nearly hemispherical. During the ex- 
periments the pitch of the principal tone was about 120 vi- 
brations per second. The vibrations were excited by a small 
wooden hammer, such as is used for harmonicons, the head 
being covered with cotton-wool tied on with string. For 
the graver tones the thickness of the cotton wool may with 
advantage be greater than for higher tones. 

Iam not in a position to decide the question as to the 
function of the shell; but I think it at least doubtful whether 
it introduces any really advantageous modification into the re- 
lations of the component tones. It is possible that its ad- 
vantage lies rather in obstructing the flow that would other- 
wise take place round the edge of the membrane. It must 
be remembered that the sounds due to the various parts of 
a vibrating membrane interfere greatly. In the case of a 
membrane simply stretched upon a hoop, and vibrating away 
from all obstacles, no sound at all would be heard at points in 
the prolongation of its plane. And even when there is a shell, 
no sound would be heard at points on the axis of symmetry, at 
least if the symmetrical vibrations may be left out of account. 


The Aolian Harp. 


So far as I amaware, it has always been assumed by writers 
who refer to this subject that the vibrations of the string are 
in the plane parallel to the direction of the wind ; and, indeed, 
the action of the wind in maintaining the motion is usually 
explained as the result of friction, and as analogous to the 
action of a violin-bow. It is more than a year since I made 


‘some experiments with the view of testing a suspicion of the 


incorrectness of this view ; and I then arrived at the conclusion 
that the vibrations are in fact executed in the plane perpen- 
dicular to the direction of the wind. I suppose for simplicity 
that the length of the string is perpendicular to the direction 
of the wind, as is usually the case in practice. Recently lL 
have repeated these experiments in an improved form, and 
with confirmatory results. 

The best draught is that obtained from a chimney. In my 
later experiments a fireplace was fitted with a structure of 
wood and paper, which could prevent all access of air to the 
chimney, except through an elongated horizontal aperture in 
the front (vertical) wall. The length of the aperture was 
26 inches, and the width 4 inches; and along its middle a 
gut string was stretched over bridges. The strength of the 
draught could be regulated by slightly withdrawing the 
framework from the fireplace, so as to allow the passage of 
air to the chimney otherwise than through the slit. 


162 Dr. J. Hopkinson on High Electrical Resistances. 


A fine point of light was obtained from a fragment of a 
silvered bead attached to the string with wax, and illuminated 
by a suitably placed candle, and was observed in the direction 
of the length of the string through an extemporized telescope. 
In this way there could be no mistake as to the actual plane 
of vibration, or uncertainty as to the direction of the wind 
over the string. The path of the point of light was seen to 
be nearly rectilinear and vertical, showing that the vibration 
is across the wind. Sometimes the path was sensibly elliptic 
with the major axis vertical. 

When a string is stretched across the slit a the bottom of a 
slightly open window, there is usually some difficulty in de- 
termining the actual direction of the wind where it plays upon 
the string. On a still night, and with a regular fire, the 
sound is sometimes steady for a long time, but it is wonder- 
fully sensitive to the slightest changes in the draught. On 
one occasion it was found impossible to open a distant door so 
slightly as not to stop the sound, which would revive in a few 
seconds after the door was closed again. A piece of paper 
no larger than the hand thrown upon the fire (which was 
burning without flame) altered the draught sufficiently to stop 
the sound until the heated air due to its combustion had 
passed up the chimney. It is the irregularity, and not, as has 
been asserted, the insufficient intensity, of the wind which pre- 
vents the satisfactory performance of the harp in the open air. 


Terling Place, Witham, 
Feb. 8, 1879. 


XXVIII. On High Electrical Resistances. 
By J. Horxinson, F.R.S., D.Se.* 


: oe the Philosophical Magazine of July 1870 Mr. Phillips 

describes a method of readily constructing very high 
electrical resistances. A pencil-line is ruled on glass; the 
ends of the line are provided with the means of making elec- 
trical connexion ; and the whole is varnished: by this means a 
resistance of ae million ohms was obtained; and it was found 
to be constant under varying potential. This method of con- 
structing resistances is alluded to in Maxwell’s ‘ Hlectricity ’ 
(p. 392); but I do not know that it has received the exami- 
nation it deserves, or that it has come into general use. Having 
need of resistances of over 100 million ohms, I have made a 
few on Mr. Phillips’s plan, ranging from 26,000 ohms to 
96,000,000 ohms (which are fairly satisfactory), and one or two 


* Communicated by the Author. 


Dr. J. Hopkinson on High Electrical Resistances. 163 


much greater (which do not conduct according to Ohm’s law, 
but with a resistance diminishing as the electromotive force 
increases). A short description of these may perhaps save a 
little trouble to others who desire tolerably constant high re- 
sistances. 

All my resistances are ruled on strips of patent plate glass 
which has been finished with fine emery, but has not been 
polished. ‘The strips are twelve inches long, and, except in the 
cases specified below, about half an inch wide. One or more 
parallel lines are ruled on each strip, terminating at either end 
in a small area covered with graphite from the pencil. The 
strip of glass, first heated over a spirit-lamp, is varnished with 
shellac varnish, excepting only these small terminal areas, 
which are surrounded by a small cup of paraffin-wax to con- 
tain mercury to make the necessary connexions. To secure 
better insulation, feet of paraffin or of glass covered with pa- 
raffin are attached on the underside at the ends of the strip 
to support it from the table. Before varnishing, each strip was 
marked witha distinguishing letter. The strips marked g, h, 7, a, 
and 6 were ruled witha BB pencil, the remainder with a HHH. 

These resistances appear to be not quite constant, but to 
vary slightly with time, the maximum variation in four months 
being slightly in excess of } per cent. In every case they 
were examined under varying potential to ascertain if they 
obeyed Ohm’s law. With the exception of f, described 
below, all were satisfactory in this respect. The resistance 
appears to diminish slightly as the temperature rises; but this 
conclusion rests on a single rough experiment, and must be 
regarded as uncertain. 

The values of the resistances were determined with a dif- 
ferential galvanometer, each coil having a resistance of 3500 
ohms, by the well-known method of dividing a battery-cur- 
rent, passing one part through the large resistance to be mea-~ 
sured and one coil of the galvanometer, the other through a 
set of coils or other known resistance, and then through the 
galvanometer shunted with a second set of resistance-coils. 
g was thus compared with standard coils. g was then used to 
find h and 7; and h+i was used to findaand 6. A Thomson’s 
quadrant electrometer was used to compare in succession &, J, 
and m with a+b. c¢ and e were similarly compared with 
k+l+m; and, lastly, c and e were used to examine sp 

g is ruled on a strip one inch wide, rather more than half 
the surface being covered with graphite. Three experiments 
on the same day gave 26,477, 26,461, and 26,470 ohms; the 
variations are probably due to uncertainty in the temperature- 
correction, the galvanometer-coils being of copper. After the 
lapse of four months 26,615 ohms was obtained. 

2 is ruled on a strip three quarters of an inch wide, with nine 


164 Dr. J. Hopkinson on High Electrical Resistances. 


tolerably strong lines; its resistance was first found to be 
209,907 ohms, and four months later to be 208,840. 

b has four strong lines on a strip half an inch wide; resist- 
ance 207,954 on a first bene and 208,750 after the lapse 
of four months. 

a has two lines narrower than the preceding; resistance 
5,240,000 at first, and 5,220,800 after four months. 

h has a single line apparently similar to either of those of a; 
and the resistance is 9,168,000. 

k, l, and m have each two lines ruled with a HHH pencil ; 
their resistances are respectively 23,024,000, 14,400,000, and 
13,218,000 obms. 

c and ¢ also have two lines, but they are finer; the resist- 
ances are 79,407,000 and 96,270,000. 

As already mentioned, all the preceding were tested with 
various battery-power, and were found to obey Ohm’s law 
within the limits of observation. It was not so with f, as the 
following observation shows very clearly. c, k, e, and f were 
arranged asa Wheatstone’s bridge. Junctions (f, c) and (e, k) 
were connected to the poles of a Daniell’s battery varying 
from one to eighteen elements; junctions (e,f) and (4,c) 
were respectively connected through the reversing-key wit 
the quadrants of the electrometer. The potential of one Da- 
niell’s element was represented by 270 divisions of the scale 
of the electrometer. Column I. gives the number of elements 
employed, II. the corresponding reading of the electrometer, 


III. the value of “= ——"— deduced therefrom, and IV. the 


fre 
values of the ratio resistance of f: resistance of e. 
I iT. IIL. EY: 
J 16 0-060 Dal 
2 25 0-046 A°6 
3 blk 0:039 4:4 
4 dl 0-029 “Ard 
5 28 0-021 3°9 
6 274 0017 3:8 
9 LO: 0:0041 3°5 
12 — 9 —0-0016 a4 
15 —25 —0°006 3°3 
18 —AT7 —0°0097 3°25 


This result is by no means surprising. There is doubtless 
an exceedingly minute discontinuity in the fine line across 
which disruptive discharge occurs; and the moral is, that re- 
sistances of this kind should always be tested as regards their 
behaviour under varying electromotive force. 

Several attempts to rule a line on a strip 12 inches long with 
a resistance over 100,000,000 ohms resulted in failure. 


pr 165"* 


XXIX. Methods of Measuring Electric Currents of great 
Strength; together with a Comparison of the Wilde, the 
Gramme, and the Siemens Machines. By Jounx Trow- 
BRIDGE, Harvard University*. 

[Plate VIII. figs. 1 & 2.] 


S haeg measurement of electric currents of great strength 
can be classed under four heads:—No. 1. The Galvano- 

metric method ; No. 2. The Hlectrometer Method; No. 3. The 

Heat Method ; No. 4. The Electrodynamometer Method. 


No. 1. The Galvanometric Method. 


With a galvanometer of small resistance and of large radius, 
it is necessary to bring the deflection to the neighbourhood of 
45° by means of a shunt of very small resistance. The errors 
increase when the deflections exceed 45° in a divided circuit ; 
and by the use of a shunt of small resistance, any error in the 
measurement of this small resistance multiplies the whole ob- 
servation by this error. 

By the use of a cosine galvanometer which I devised in 
1871, and published in the ‘American Journal of Science’ 
for that year, the use of shunts can be modified; but there are 
difficulties, from the dip of the needle and from want of accu- 
racy in graduations of the circle which measures the deflection 
of the moving coil from the vertical plane. 

In practice it is very inconvenient to find a suitable shunt 
which will answer for a wide range of experiments, and diffe- 
rent shunts have to be used. Moreover the heating of the 
shunt multiplies the observations by an error. In short, by 
the use of a shunt method, we measure a large quantity by 
observations upon a hundredth or a thousandth part of itself, 
and proceed from a small quantity to a large one, which is a 
fundamentally defective method. 


No. 2. The Electrometer Method. 


By means of a suitable electrometer, the difference of po- 
tential of two points in a closed circuit can be measured ; and 
from this the electromotive force in volts can be estimated. 
The difficulty of dealing with static electricity in electrical 
measurements is well known. Leakage, want of constancy of 
charge in the electrometer, nay, impossibility of maintaining 
a charge in certain localities, limit the use of this method, 
even if the results obtained were not approximate. 


* From the Proceedings of the American Academy of Arts and Sciences, 
New Series, vol. vi. pp. 122-132. Communicated by the Author. . 


Phil. Mag. 8.5. Vol. 7. No. 42. March 1879. oF 


166 Prof. J. Trowbridge on Methods of Measuring 


No. 3. Heat Method. 


By the use of the law that the heat developed in a circuit 
is expressed by H=C’R¢#, where C is current in Vebers, R= 
resistance, ¢=time, we can deduce C by measuring the rise of 
temperature of a given volume of water. Measurements of 
temperature are especially fraught with difficulties on account 
of conduction, radiation, and errors of thermometers, beside 
consuming time in waiting for the proper conditions for a 
given experiment. : 


No. 4. The Electrodynamometer Method. 


The principle of Weber’s electrodynamometer is well known. 
The electric current passes down one wire of the bifilar sus- 
pension of a movable coil and up the other, and then through 
fixed coils surrounding the movable coil. Maxwell, in his 
‘Hlectricity and Magnetism,’ vol. ii. p. 3832, remarks :— 
“Weber’s form of the electrodynamometer, in which one coil 
is suspended within another, and is acted on by a couple tend- 
ing to turn it about a vertical axis, is probably the best fitted 
for absolute measurements.” With powerful currents, how- 
ever, it is necessary to shunt this instrument, and the errors 
inherent in this method are introduced. Hyven with moderate 
currents, the directive force of the bifilar suspension is changed 
by the elongation of the wire from a rise in temperature. If 
we keep within the point at which the wires are elongated, 
the deflections are slight and subject to error of observation. 

In working with dynamo-electric machines, it is important 


that we should avoid the method of shunts; for the entire - 


resistance of the circuit is generally of the same order of mag- 
nitude as the shunts employed. It is necessary that we measure 


the whole strength of the current directly at the same time that - 


we measure the work consumed in driving the dynamo-electric 
machine, the velocity of the machine, and the resistance of the 
circuit. It is also important to eliminate local attractions. 
The time consumed in measuring the current-strength should 
be small. 

The instrument described in this paper fulfilled the condi- 
tions prescribed. 

Fig. 1 (Pl. VIII.) shows the general aspect of the apparatus. 
The large fixed coils were made of copper bands, 35 millims. 
broad and 1 millim. thick. There were twelve coils, six on 
each side of the movable coil, which is shown with its suspen- 
sion between them. The large coils we reinsulated from each 
other by vulcanite washers, and held together by brass rivets 
insulated by vulcanite cylinders. The coils were placed at a 
distance apart equal to their thickness, and thus allowed cur- 


— 


Electric Currents of great Strength. 167 


rents of air to pass freely between them. This arrangement 
is shown at I (fig. 2). The bifilar suspension is connected 
with a graduated circle which reads by means of verniers to 
oneminute. The tangent and clamping-screws of the torsion- 
head are not shown in the figure. ‘The general arrangement 
was similar to that used by Mr. Latimer Clark, and figured in 
Maxwell’s ‘ Electricity,’ with the exception that the gradua- 
tion was not upon a cylinder, but was on a plane, and the gra- 
duated circle was such as is used on spectrometers. The 
torsion-head admitted of vertical adjustment by means of the 
hollow cylinders at its point of support, in addition to the ver- 
tical adjustment of the pulley by means of which the tension 
upon the suspending-threads was equalized. In the ordinary 
form of electrodynamometer the current passes down one 
suspending-wire and up the other. In my dynamometer this 
is not the case, as is shown in fig. 2. Therefore the suspen- 
sion can be made of strands of silk or any suitable material, 
according to the sensitiveness desired. In the actual use of 
the instrument with powerful current, it was found necessary 
to use steel wire, in order to increase the directive force, so 
great were the deflections. 

The movable parts are best shown in fig. 2. The construc- 
tion of the central coilis shown at D. The water enters at a, 
passes out at a after cooling the hollow chamber B, which ad- 
mits of adjustment, and then flows by rubber tubing to f, and, 
after cooling the mercury-cup E, flows out through/f. G is 
the water-chamber which answers to B. At n, below the 
mirror m, is a bar upon which are hung cylindrical weights 
to determine the moment of inertia to alter the sensitiveness. 
Only one coil anda half are shown in the figure. The electric 
current enters at H, passes through the mercury-cup to E, 
then to C, and thence by the hollow cup to O, and then around 
the outer coils. 

A telescope with scale was employed to read the deflections; 
but it was found better, in practice, to use the graduated 
circle of the torsion-head and bring the movable coil back to 
zero. In this case we have, from the theory of the electrody- 


namometer, pe 
C= ap H sin 0; 
Gg 


and the effect of the earth and local attraction are eliminated, 

By this method of observation no telescope and scale are 

needed: it is only necessary to bring the point of the bar 

which passes through the movable coil to a fixed point. The 

mercury in the pivot-cups oes to damp the vibrations of 
2 


168 Prof. J. Trowbridge on Methods of Measuring 


the movable part of the apparatus ; ; and it was found that read- 
ings could be taken quicker than by galvanometric methods. 


Theory of Instrument*. 


F tan 0 


2 
x Gy cos 8’ 
where 
C = current, 
F = directive force, 
G and g = constants of fixed and movable coils, 


8 = angle of coil with magnetic meridian. 


If the torsion-head of the instrument can be ds so that 
the deflection is zero, and 6= —8, we have 


iy 
4 1 
C— Ga sin 8. 
The value of F was determined by several methods. Since 


Bea A. 
where 
t is the time of vibration, 
and 
A= moment of inertia, 


it is necessary to determine both the time of swing and the 
inertia. The times of swinging were obtained by means of a 
chronograph upon which seconds were recorded by the side of 
the records produced by breaking an electric circuit at the in- 
stant the movable coil passed the middle of its vibration. 
The moment of inertia was first determined experimentally by 
adding known cylindrical weights and seve the new 


time of vibration. 
2 
ay eae tl 
(1 +—?-—? 
Wy 


We thus have 
2 2 fie 
k=w (2 a5 ei 


where k = moment of inertia of added cylindrical weights, 
w = weight of cylinders in milligrammes, / = distance of 
point of suspension of cylinders from axis, r = radius of cy- 


and 


* Maxwell’s ‘ Electricity,’ vol. ii. p. 329. 


Electric Currents of great Strength. 169 


linders, and w, mass of moving parts before w was added ; the 
dimensions being in millimetres. 
From these expressions we obtain 


PTE, 
ee 52 
(1+ =) et 


The constants G and g were calculated from the actual 
measurements of the coils, which could be made with great 
accuracy, since all the parts were large. 

The constants were as follows :— 


mean radius r= 153°3 millims. 
Gg=1631:45_,, 
a = 6567626 ,, 
The constant was also determined by running the same 
current through the electrodynamometer and a tangent gal- 
vanometer of one turn of copper wire, whose radius was 7, 


and whose constant was equal to ot 
2ntr 


In this case 


7T? pee 
C= Teg tan” d= Ges d, 
and 
Hoe i tans O 
Gg 4n?x* sind ’ 
where 


T= horizontal force of earth’s magnetism, 
r= radius of galvanometer-coil, 

@= deflection of galvanometer, 

$= deflection of electrodynamometer. 


The result obtained in this way closely agreed with that ob- 
tained by the previous method. 

No difficulty was experienced from the heating produced 
by currents of even eighty vebers when the current was 
allowed to run for a long period through the instrument: as 
long as the stream of water was maintained around the mer- 
cury-cups, even a small immersion of the point of the axis of 
the movable part of the instrument did not result in heating. 
By this instrument, therefore, the whole current could be 
measured without shunting. At first the metal pivots which 


(170 ~~ Prof. J. Trowbridge on Methods of Measuring 


dipped in the mercury were tipped with aluminium; but 
when a strong current passed through them the mercury was 
disturbed by an apparent ebullition, and the mercury was 
speedily covered with a black deposit. It was found that 
copper points would answer perfectly well. Distilled mereury 
was used in all cases; it answered the double purpose of con- 
ducting the current and bringing the vibrations quickly to 
rest. 

Through the courtesy of Captain Breese, U.S.N., in charge 
of the U.S. Torpedo Station at Newport, R. I., who obtained 
permission for me to use the dynamo-electric engines at that 
place, I was enabled to make a series of measurements with 
the dynamometer described above. 

The resistances used consisted of large bands of German 
silver, each in the neighbourhood of ;!; of an ohm resistance. 
The foot-pounds of work consumed were measured by a Bat- 
chelder’s dynamometer*, which is fully described in Dingler’s 
‘Polytechnic Journal,’ 1844, vol. 11. This dynamometer is 
not suitable for the measurement of small or great horse- 
power ; but it answered very well in the limits of velocities 
and horse-powers to which I confined myself. An accurate 
measure of the work consumed in running a dynamo-electric 
machine upon a closed circuit would require the use of gear- 
ing instead of belting; for it is difficult to estimate the slip of 
the belting. On account of the error introduced from this latter- 
mentioned cause, I have given the whole work required to run 
each machine on a closed circuit. The slip on an open circuit 
would be small, but on a closed circuit might be very large. 
The machines were run under the same conditions of shafting 
and pulleys. It was estimated that the Siemens required 
0-031 horse-power on an open circuit, and the Gramme 0°206 
to 0°328 horse-power. ‘The term efficiency denotes the ratio 
of the equivalent in metre-grammes of the current produced 
to the metre-grammes consumed in running the dynamo-elec- 
tric machine. Since one veber through one ohm 

10° 
= C = io? = LO 
the work w=C?Rt=(10-?)? x 10’=10®=1000 units of work ; 
and dividing by the unit employed, we have 


equivalent of 1 veber = 102 metre-grammes, 
1 foot-pound = 138 


7) 


‘ * For which I am indebted to the Massachusetts Institute of Techno- 
ogy. 


Electric Currents of great Strength. ee 
Wilde Machine (large size). 


Resistance of | Current, in | Speed of | Metre-grammes Equivalent of 


are . 5 : current in metre- 
circuit, in | vebers per | machine, per| consumed per grammes per 
ohms. second. minute. second. Aneel 
O94 62°33 548 350°658 235-480 
"733 61-76 508 392403 285293 
"857 43°82 532 283°107 167-907 
"907 60°25 500 453°123 335°966 
1:039 39°28 520 298° 356 163°682 
1-120 43°44 548 343°827 215-660 
1-241 50°43 504 542-685 322-047 
1-453 44-94 520 553311 309-658 
1:593 47°51 536 633°765 366'910 
2°305 82°86 528 643°632 253:968 


The measurements with the Wilde machine were made with 
an electrodynamometer similar to that described in Maxwell’s 
‘Electricity and Magnetism. It was constructed on the 
Helmholtz-Gaugain principle, and had a resistance of 58-9 
ohms. A shunt of ‘1 ohm had to be employed; and the in- 
strument was also coupled in multiple arc to avoid the length- 
ening of the bifilar suspension. 


Gramme Machine (large size). 


Resistance of | Current, in a ber of jeer ee a 
circuit, in vebers per pe vo wos Ot onsumed per Pier an eee 
Fikes Ee Na armature per oe grammes per 
; ; minute. a a second. 
‘675 86:0 432 589-743 509-418 
‘760 756 462 534-336 449-211 
“781 756 452 607°200 455°377 
Siemens Machine (large size). 
5 
‘973 79°83 264 831-105 632°255 
1-055 68:8 294°5 743°820 509-569 
1-066 66:0 320 839°454 472°805 


I add a few data in regard to the dimensions of these ma- 
chines, which are partly taken from the reports of the Secre- 
tary of the Navy for 1877, and partly from the Station records, 
which were generously placed at my disposal. — 

The Gramme Machine-—This machine weiglis about 2700 
pounds, stands 30” high, is 40” long and 34” wide. It is 
driven by a pulley 15” in diameter. The armature moves 
with very little friction. The field-of-force coils are flat; and 


172.) On Measuring Electric Currents of great Strength. 


there are four of these, each about 10” long, 32” deep, and 
22’ wide. The armature resistance is 0°129 ohm, the field 
resistance 0°212 ohm, thus making °341 ohm for the total 
internal resistance. The total weight of wire in the machine 
is 483 pounds; or the weight of wire is nearly 18 per cent. of 
the total weight of the machine. 

Siemens Machine, or Heffner-von-Altenek Machine, built 
by the Siemens Brothers.—This machine is 61” in length, 28” 
in breadth, and 12” in height. The armature is nearly 34” 
long and 93” external diameter. It is formed by winding 98 
pounds of two insulated wires longitudinally, and in eight di- 
visions, around a thin and hollow brass cylinder. Within this 
hollow cylinder is a hollow stationary cylinder of cast iron, 
supported by bearings that pass through the brass cylinder. 
The commutator has eight divisions, which are eight sector- 
shaped sheets of brass, insulated from but attached to the face 
of a plate which is outside of one of the bearings of the brass 
cylinder. Two collectors or brushes trail upon and press 
against these sectors: these brushes have a bearing so exten- 
sive as to short-circuit or bridge over the edge of two sectors. 
The spark of the commutator is quite insignificant. This ma- 
chine differs from all others in this respect—the armature 
simply moves a wire through a field of force, and not a soft- 
iron core covered with wire. ‘The resistance of the entire 
circuit, field of force, corrected for conductivity, is 586 ohm. 
The normal velocity of the machine is from 370 to 380 revolu- 
tions per minute. 

Wilde Machine.—This resembles in some respects the Hjorth 
machine of 1855 with the permanent magnet omitted. It has 
two armature circuits—one with current uniform in direction 
for the purpose of maintaining the magnetism of the field, and 
the other for producing the electric light. The current from 
this last circuit is a to-and-fro current, without commutator. 

‘¢ The armature wire weighs 28 pounds, and is divided into two 
circuits: about 7 pounds of it, having a resistance of -454 ohm, 
furnishes the current which maintains the field. The remainder 
(21 pounds), having a resistance of ‘(074 ohm, maintains the 
to-and-fro current. About 325 pounds of wire are distributed 
in 24 coils to make up the electromagnetic field, which has a 
resistance of 2°83 ohms. These coils are 101” in length and 
3%” in external diameter, having soft round cores 2” in dia- 
meter. ‘There are 24 armature cores and coils, one half on 
each side of a central cast-iron wheel 14” thick. The central 
diameter of this wheel is 18” nearly. The whole weight of 
wire in this machine is nearly 354 pounds.” The normal 
velocity of the machine is about 600 revolutions. A greater 


Rotation of the Plane of Polarization of Light. 173 


rate of speed would have increased, to a certain extent, the cur- 
rents produced by the Siemens and the Gramme machines ; on 
the other hand, more horse-power would have been necessary 
to attain this increased speed. The Wilde machine requires 
more horse-power to run it as the resistance of the outside 
circuit increases. This is due to the construction of the ma- 
chine, and is not the case with the Siemens and the Gramme 


machine. A certain proportion between the resistance of the 


machine and that of the outside circuit is undoubtedly best 
for greatest efficiency of dynamoelectric machines ; and a cer- 
tain velocity is necessary to attain the greatest efficiency. 
From my experiments, I should class the machines as fol- 
lows:— 
Gramme, 
Siemens, 


Wilde. 


Theoretically the Siemens machine should give the best 
results. At the time of my experiments the Siemens machine 
suffered the disadvantage of being run at a less rate of speed 
than the other machines. 

I hope to pursue these tests under conditions resulting from 
higher speed. Generally speaking, that machine is the best 
which gives the greatest efficiency at low rates of speed ; for 
the necessity of high speed introduces much that is detrimental 
to the locality of the machine and to the machine itself. At 
the present time alternating machines are coming into notice 
again, in connexion with electric lighting; and a suitable elec- 
trodynamometer is desirable in the measurement of the current 
produced by these machines. The instrument which I have 
tested above seems to fulfil the proper conditions. 

My thanks are due to the officers of the station for their 
generous assistance and free disposal of the resources of their 
electrical department. 


XXX. A Proof of the Electromagnetic Rotation of the Plane 
of Polarization of Light in the Vapour of Sulphide of Carbon. 
By A. Kunpt and W. C. RéntcEn*. 

[Plate VIII. fig. 3.] 
ARADAY, as is well known, did not succeed in demon- 
strating the electromagnetic rotation of the plane of po- 
larization of light in gases ; and since his time that a rotation 
has not been observed. 


* Translated from a separate impression, with an original postscript, 
communicated by the Authors, 


174 MM. Kundt and Rontgen on the Electromagnetic 


On account of the interest presented by the question whether 
this property does not belong to gases in general, we resolved 
to repeat the experiments once more with the most powerful 
currents and, in all other respects, under the most favourable 
conditions; and we have now succeeded in verifying the 
phenomenon sought, at icast for the vapour of bisulphide of 
carbon. 

We selected this substance for the experiments because, on 
the one hand, in the liquid state it exhibits an energetic elec- 
tromagnetic rotation, and, on the other, its vapour possesses 
considerable tension even at comparatively low temperatures. 

The apparatus employed for enclosing and heating the 
carbon bisulphide is delineated in fig. 3, Pl. VIII., one tenth 
of its actual size. An iron tube, aa, is furnished at its ends 
with two strong conically out-turned brass collars, bb; into 
these two brass pieces, ¢ c, likewise conical, can be inserted, 
and each pressed in firmly by means of six strong screws. 
The inserted pieces are perforated in the direction of the length 
of the tube (diameter of the perforations 1 centim.); and to 
the side turned towards the interior of the tube two glass | 
plates, dd, 1 centim. thick, are cemented, which are also held - 
by strong screws. To the insertion-pieces, ¢, two tin-plate 
tubes, ee, are screwed; and the whole is enclosed in the tin- 
plate tube 77, in the centre of which it is held by the two 
corks gg. The tubes ee stand out about a centimetre beyond 
the corks. By an inlet-tube, h, in one of the corks, steam can 
be introduced into the space between the iron tube and the 
surrounding tin-plate tube ; through a tube, 7, in the other 
cork itcan pass out again. Consequently the iron tube could, 
by steam led round it, be heated in its entire length to 100°. 
The outer tin-plate tube was enclosed in six large coils of 
wire. 

The wire was of 3 millims. thickness. ; in each coil there 
were about 400 turns, through which the current of 64 large 
Bunsen cells could be sent. 

For the experiment some bisulphide of carbon was poured 
into the iron tube, and the air expelled by the carbon-bisulphide 
vapour already forming at the ordinary temperature. Then 
the inset pieces were screwed as fast as possible to the ends, 
the tube with its appendages was fixed in its place inside the 
wider tin-plate tube and the spirals, and steam introduced. 
As soon as the entire tube had acquired the temperature of 
boiling water, all the mist that had appeared on the glass 
plates during the heating vanished, and the plates and the 
sulphide-of-carbon vapour that had formed in the tube were 
perfectly transparent. A rectilineal pencil of light, polarized 


Rotation of the Plane of Polarization of Light. 175 


by a Nicol, was now sent through the vapour; a Nicol at the 
other end extinguished the pencil. The current of the 64 ele- 
ments was now sent through the coils, when the field was 
distinctly brightened. The brightening was still more consi- 
derable when, after the closing of the current, the front Nicol 
was rotated to darkness and the current then reversed by a 
commutator. 

The rotation of the polarization-plane took place, as was to 


be expected, in the direction in which the positive current 


went through the coils. 

In order to find out whether the observed rotation might 
not be entirely or in part produced by the glass plates that 
closed the ends of the tube, the sulphide-of-carbon vapour was 
expelled, and the empty tube again heated and observed. On 
closing the current there was in fact shown a very slight rota- 
tion proceeding from the glass plates; but its amount was 
essentially less than when the experiment was made with sul- 
phide of carbon in the tube. In order to get quite rid of this 
feeble glass-plate rotation, the two outermost coils (those 
nearest to the plates) were put out of the circuit, and the 
four through which the current still passed were now removed 
so far from the glass plates that their influence upon the latter 
could only be extremely slight. It was in fact now found that 
the empty tube, heated by steam, showed no trace of rotation. 
But when the tube was again filled with sulphide-of-carbon 
vapour, at the closing of the current through the four coils a 
distinct brightening of the field of vision, previously darkened 
by crossing the Nicol, was obtained. We could not measure 
precisely the amount of the rotation: we estimated it in the 
last experiment at about 4°. 

By this it is demonstrated that saturated vapour of bisulphide 
of carbon, at about 100° C., rotates the plane of polarization of 
light in the magnetic field. | 

When some sulphuric ether was put into the iron tube and 
heated, on closing the current no rotation could be observed. 

Although, it is true, by our experiments it has at present 
been shown only that saturated bisulphide of carbon exhibits 
electromagnetic rotation of the plane of polarization, yet it is 
now hardly to be doubted that it will be possible to prove the 
existence of the polarization in unsaturated vapours and gases 
also. We are engaged in the construction of an apparatus 
which shall permit us to examine permanent gases at very 
high pressures in the magnetic field, in order to demonstrate 
the rotation for these, and, if possible, to follow up the phe- 
nomenon with measurements. 

Tt will be especially interesting to ascertain whether oxygen 


176 Mr. W. J. Lewis on the Analysis 


rotates the plane of polarization in the same direction as the | 
other gases. 


Strasburg, October 1878. 


Postseript.—Since the publication of the foregoing experi- 
ments we have further improved the apparatus employed, b 
giving to the iron tube (aa in the figure) a length of 2-4 
metres. ‘The glass plates dd were now so far from the ends 
of the six coils that, on closing a current from 70 large Bun- 
sen elements, they did not produce any perceptible rotation. 
A repetition of the experiments with bisulphide-of-carbon 
vapour gave now also an evident rotation of the plane of pola- 
rization. | 

In like manner we succeeded in observing the electromag- 
netic rotation in gaseous sulphurous acid at 100° C. and a 
pressure of about twenty atmospheres, and in sulphuretted 
hydrogen gas at the ordinary temperature and about twenty 
atmospheres. 

In air, up to twenty-five atmospheres, we have not yet been 
able to observe any rotation. We wi!l not omit to remark 
that, apart from employing very high pressures, another way 
presents itself of making the observations for the investigation 
of the rotation in air—with polarized sunlight, which with 
the aid of heliotropes in the direction of the earth’s magnetic 
meridian is sent through a long stretch of the atmosphere. 


XXXI. Note on the Analysis of the Rhombohedral System. 
By W. J. Lewis, MA., Fellow of Oriel College, Oxzford™. 


fea methods followed by Professor Miller and most writers 

for obtaining the formule employed in determining the 
indices of a form in the rhombohedral system from the mea- 
sured angles, or, conversely, the angles from the given indices, 
are, though elegant, difficult and perplexing. It occurred to 
me that they might be easily obtained by means of the anhar- 
monic ratio of four poles in a zone applied to three known 
poles in one of the planes of symmetry, and a fourth pole 
whose position and indices can be directly connected with the 
poles of the form to be determined. This method brings out 
in a prominent manner the relation (2); a relation to be found 
in all the books, but so disguised and so little noticed as easily 
to be passed over, whereas from its simplicity, and from the 
fact that the angle involved in it is the first deduced from the 


* Communicated by the Crystallological Society. Read Nov. 24, 
1878. 


of the Rhombohedral System. 177 


measured angles of a scalenohedron, it contains a smaller error 
than any other equation. 

The figure represents the stereo- 
graphic projection of some of the 
principal poles and planes of a 
rhombohedral crystal, together with 
the poles P of a form {hk 1} to be 
determined. The poles r are {100}, 
o(111); therefore the poles 6 and a 
are {21 lt and {011} respectively. 
er P be (41), P,, P,, the corre- 
sponding faces repeated over O06 
and Ob,. Then P, is (klk), and 
P,,(khl). Let Q, R, 7 be the intersections of the pairs of 
zones [PP,] [Ob], [PP,,] [0b,,], [OP] [00,,] respectively. 
Then the indices of Q are (2h, k+/1, k+1), of R (A+h, A+h, 
21), and of 7 (2h—k—1l, —h+2k—l, —h—k+21.) 

The anharmonic ratio of the poles a, b,,, 7, b gives 


sinbar | sinbb,/ _ | Pel _ kl 
sinma’ sinb,a Lal Lb,al~ 2h—k—l 
(Miller’s ‘ Treatise on Crystallography,’ p. 14). Hence 


ae: _ &-)V3 1 
tan dr=tan XOP= ry ey a Mae (1) 


The anharmonic ratio of the poles O,7, Q, b gives, in a similar 


manner, 
tanOQ_ FOQ]. oa] — 2h—k—l | 
tan Or =! : = — QA+k+T)’ 
and writing D for the element Or, we have 
2h—-k—l 
tan OQ= WhER+D tan D. Aira e (2) 


Similarly from the poles O, R, b,,,and z (22 1) the dirhombo- 
hedral face of r,, we obtain 
tanOR _ =: 2) = h+k—2l 9/ 
tat PE yd les: ~ WA+k+AD * 7) 
From the right-angled triangle POQ we have 
tan OP= tan OQsecbr; . . . . (A) 
*. from (1) and (2), 
ee coats Sin et) sical (om rv 


fas 2b R+1Y o) 


178 On the Analysis of the Rhombohedral System. 


The equation (2) is given by Professor Miller in his ‘ Trea- 
tise on Crystallography,’ 1839, in the form 


2h—k—l 
tan PO tan XO cos KOP= ee 
and in the equivalent form | 
2 tan PO cot OA cos XOP= So 
hAt+k+l 


the latter being the same as (2), with the sole difference that 
tan OQ is replaced by its value given by equation (A). The 
form in which it is given by Professor Miller does not, how- 
ever, bring out so prominently the simplicity and directness 
of the relation existing between the quantities involved in the 
equation and those given by observation. 

As an illustration of the utility of equations (2) and (2’), 
let us take the determination of a scalenohedron on a mineral 
(such as calcite) whose elements are known.. Measurement of 
two of the angles between adjacent faces suffices for the deter- 
mination. If PP, and PP, are the two angles measured, we 
know the three sides of the triangle aPa,; and the angle 


Pab=bQ= 5 —OQ is the first quantity deduced from the 


measurements. [Equation (2) then gives a simple equation in 
terms of the indices h, k, 7. If PP, or PP,, be given with the 
angle of the middle edge of the scalenohedron, we know the 
sides of the triangles aPa or a,,Pa, In the first case OQ is 
determined as before, in the second OR; and we must employ 
(2) or (2’) accordingly. 

To complete the analysis, I need only point out that the 
relations connecting the indices of dirhombohedral forms can 
be most simply obtained by aid of the equations connecting 
the indices of a face with those of the zone in which it lies. 
Thus EH, the face of the dirhombohedral form corresponding to 
P, lies in the zones [OP] and [6,P,,], whence its indices can 
be at once obtained, and all the geometrical relations connect- 
ing it with P can be proved. Professor Maskelyne has, I 
believe, already given this method of deducing the indices of 
the dirhombohedral form in his lectures at Oxford. 


—— 


| 


ba d7gs 


XXXII. On Mr. G. F. Fitzgerald’s Paper “On the Mechanical 
Theory of Crookes’s Force.’ By Osporne REYNOLDS, — 
eS.” 


_ FITZGERALD appears to have overlooked the fact 
that my paper in the Proceedings of the Royal Society, 
1874, “On the Surface Forces caused by Hvaporation and 
Condensation,” was published more than a year before Mr. 
Crookes published any account of the radiometer; otherwise 
he certainly would not have fallen into the error of supposing 
that I had concluded that the motion of the arms of the radio- 
meter was mainly due to evaporation and condensation. That 
such actions cannot explain continuous motion is at once ob- 
vious. Butthen Mr. Fitzgerald fails to notice that on the first 
page of my paper an experiment is described which proves this 
very point; and he also fails to notice that all the phenomena 
I have considered in any way due to evaporation and conden- 


- sation were essentially intermittent. 


It would appear that Mr. Fitzgerald has not read my paper; 
for after stating that the method by which I “tried to show 
that a surface, when communicating heat to gas, is subject to 
an increased pressure is open to the overwhelming objection 
that this increased pressure would be almost instantaneously 
transmitted to all parts of the enclosed gas,’’ he devotes some 
fourteen pages to the attempt to prove the very same thing. 

To point out these errors in Mr. Fitzgerald’s statements 
constituted my main object in writing this note ; but I would 
say a few words on the subject in question and Mr. Fitz- 
gerald’s treatment of it. 2 

Mr. Fitzgerald bases his theory on Mr. Stoney’s view that 
the phenomena of the radiometer are to be explained by the 
fundamental assumption “that when two surfaces at different 
temperatures are in presence of one another with a gas between 
them, there exists a force terding to separate them.’’ Assu- 
ming that it is here meant that the gas should surround the 
surfaces and not merely exist between them, it may appear. at 
first sight as though this assumption would explain the pheno- 
mena; but on closer examination it will appear, as I have pre- 
viously pointed out, that this is not the case. Under such 
conditions as are assumed the experiments show that the force 
would not tend to separate the surfaces, but such forces as 
there might be would impel both surfaces in the same direc- 
tion—showing that the force does not act between the two sur- 
faces, but between each surface and the gas which surrounds 


* Communicated by the Author. 


180 —= On the Mechanical Theory of Crookes’s Force. 


it—and that the force does not arise from the difference in 
temperature in the two opposite plates, but from the difference 
in temperature of the two surfaces of the same plate. 

It appears, then, that such a separating force as that assumed 
by Mr. Fitzgerald would not explain the phenomena in ques- 
tion, and therefore that these phenomena afford us no ground 
for assuming the existence of such a force. Any reason there 
may be for assuming such a force must therefore come out of 
some hypothesis as to the constitution of gas; and in this 
respect the result of Mr. Fitzgerald’s investigation is not very 
conclusive. 

Adopting the hypothesis of Clausius, Mr. Fitzgerald’s rea- 
soning leads him to the conclusion that there is no such separa- 
ting force (see the bottom of page 22). Instead, however, of ac- 
cepting the conclusion, Mr. Fitzgerald concludes that Clausius 
is wrong :—“ It seems certain that the hypothetical distribution 
Clausius assumed is not at all adequate to represent the actual 
one.” He then proceeds to modify the expression derived 
from Clausius’ hypothesis so as to make it yield the force for 
which he is looking; but he attempts no explanation or exami- 
nation of the physical meaning of such a modification ; so 
that admitting, as I have pointed out, that we have no expe- 
rimental evidence of such a separating force, Mr. Fitzgerald’s 
investigation clearly affords us none, but, on the other hand, 
shows either that Clausius is wrong or that there is no such 
force. 

Had Mr. Fitzgerald been true to his mathematics, had he 
accepted the conclusion that there is no such separating force 
as he has assumed, and then examined the physical meaning 
of the modifications of the expressions which he has introduced, 
I venture to say that he would have found that his modi- 
fications of Clausius’ hypothesis, on the assumption that the 
direction of flow of heat is everywhere the same, would corre- 
spond with the true expressions of Clausius’ hypothesis when 
there is divergence in the directions along which heat is 
flowing. 

This divergence turns out to be an essential condition in 
order that there may be force such as that which causes mo- 
tion in the arms of the radiometer. And since the pressure in 
the direction of flow is greater or less than the mean pressure, 
according as the lines of flow diverge or converge, the pressure 
will be greater against the hot side of a plate and less against 
the cold side. 

When I first suggested that there would be an inequality 
of gaseous pressure arising from a communication of heat, I 
had not realized that, besides depending on the quantity of 


me —_ — EEE 


The Theory of Binaural Audition. 131 


heat communicated, the inequality would depend on the diver- 
gence of the lines of flow—although my explanation, so far as 
it went, was quite consistent with such a necessity. 

The importance of this divergence became clearer to me in 
November 1877; and I had no sooner recognized it than I 
perceived a general connexion between the phenomena in 
question and other phenomena of gases, particularly that of 
transpiration, or diffusion through porous plugs. I did not 
then publish any account of the theoretical investigation, be- 
cause the theory indicated the existence of other phenomena 
beyond those already known, and I wished to verify these in- 
dications of the theory by experiment. 

These experiments have occupied considerable time; but 
they are now completed, and their result is (1) to verify the 
theoretical revelations as to the existence of a class of very 
marked and important phenomena which were, so far as I 
know, previously unsuspected, (2) to establish certain general 
laws which apply equally to the phenomena of transpiration 
and those of the radiometer, and (3) to afford an absolute 
proof that gas possesses dimensional structure (7. e. that it is 
not a continuous plenum), the results of the experiments 
agreeing with those deduced from the theory in the most de- 
finite manner. <A paper containing an account of both the 
theoretical and experimental investigations has been forwarded 
to the Royal Society. 

January 28, 1879. 


XXXII. The Theory of Binaural Audition. A Contribution 


to the Theory of Sound. By Anton STEINHAUSER*. 
[Plate IX. ] 
INTRODUCTION. 
ae theory of Audition may be divided into two portions— 
that of Monaural Audition, or of hearing with one ear, 
and that of Binaural Audition, or of hearing with both ears. 
The former, already treated of in every textbook of Physics, 
is concerned with explaining the arrangement of the human 
ear, the function of its separate parts, and, lastly, how the ear 
is instrumental in the faculty of hearing. The second branch 
of the subject, which has never, to my knowledge, been yet 
developed t, has to discuss the general question of hearing, 


* Translated and communicated by Prof. Silvanus P. Thompson. 

+ [For the literature of the subject see :— 

Luca, A.—Virchow, Archiv, xxv. 1862: “Zur Physiologie und Patho- 
logie des Gehororganes.”’ 

Rayleigh, Lord.—Proe. Mus. Assoc. 1875-76: “On our Perception of 
the Direction of a Source of Sound.” 

Thompson, S. P.—Rep. Brit. Assoc. 1877: “On Binaural Audition, 


Phil. Mag. 8. 5. Vol. 7. No. 42. March 1879. |e 


182 Prof. A. Steinhauser on the Theory 


with respect in particular to the circumstance that it is per- 
formed with two ears. It is concerned, further, in deciding 
what part binaural hearing plays in the various phenomena of 
hearing in general, and the various advantages thereby gained. 


THEORY OF BINAURAL AUDITION, 


Preliminary Observations. 


The sound produced by any source of sound is, as is known, 
brought to our consciousness in the following manner :—The 
vibrations originated by the sounding body are taken up by 
solid or fluid bodies which are adjacent to it, or more com- 
monly are taken up by the surrounding atmospheric air, and 
are thence propagated until they reach either directly, or by 
reflexion, the auditory passages of our ears, and thus in- 
fluence the drumskin, the auditory ossicles, and finally the 
auditory nerve. 

Moreover an essential adjunct for fine hearing is the ex- 
ternal flap or pinna, which usually acts as a funnel, to conduct 
into the ear the vibrations which, in consequence of their di- 
rection, reach but cannotenter it. These vibrations, travelling 
through the air in straight lines, we may for brevity call rays 
of sound, by analogy with the expressions “ rays of light”’ and 
“rays of heat.”’ | 

According to the nature of the path by which the sound- 
rays reach. the single ear, we may distinguish between direct, 
indirect, and mixed monaural hearing. 

In direct monaural audition the rays proceeding from the 
sonorous body reach the ear immediately, or in straight lines, 
and enter the auditory meatus either directly or after under- 
going reflexion on the pinna or flap. . | 

In indirect monaural audition the rays proceeding from the 
source of sound do not reach the ear directly (that is to say, 
not in straight lines), but after undergoing simple reflexion on 
the ground or on some other surface, or even occasional mul- 
tiple reflexion, in which case the path travelled by the rays 
forms a zigzag line. Such a kind of reflexion is in many 
cases absolutely necessary if the rays of the sonorous body are 
to reach the ear at all. 

In mixed monaural audition the rays proceeding from the 
source of sound reach the ear partly directly, and therefore in 
straight lines, partly indirectly, or after previously undergoing 
reflexion, and consequently in zigzag lines. 


part 1. Rep. Brit. Assoc. 1878: “Phenomena of Binaural Audition,” 
part 2. Trans. Assoc. Frangaise, 1878: “Sur des Phénoménes de l’Audi- 
tion Binauriculaire.”—TRANSL, | . 


of Binaural Audition. 183 


It might conceivably appear that direct audition could only 
occur under conditions of a special character, and therefore 
extremely rarely, since the hearer is almost always surrounded 
by reflecting surfaces, amongst which, of course, the earth 
must be reckoned. ) 

Figure 1 exhibits the aspect of the human head from above, 
jf, and f, being the surfaces of the pinne.. They make with 
one another an angle 23. Hence it is easily perceived that 
according to the position which the source of sound occupies 
in the horizon of the hearer, the following cases may be dis- 
tinguished with respect to binaural audition. 

1. The source of sound may be situated within the angle 
DnC. The hearer then hears directly with both ears ; and ac- 
cordingly there exists a direct binaural audition extending 
through the angle DnC, which is equal to 28. 

2. The source of sound may be situated within one of the 
angles AnD and BnC. The hearer then hears directly with 
one ear only, whilst the other ear hears only indirectly in almost 
every case, on account of a scattering of the sound, analogous 
to the scattering of rays of light. In consequence a mixed binau- 
val audition occurs, and extends, irrespective of the region in 
which both ears hear directly, through the angle(AnD+BnC), 
which is equal to (860—4/). 

3. The source of sound may be situated within the angle 
AnB. The hearer in that case evidently hears only indi- 
rectly with both ears; accordingly indirect binaural audition 
occurs, and extends through the angle An B, which is equal to 
26. 
The 360 degrees of the entire circle within which the source 
of sound is situated are therefore disposed as follows :— 


28 degrees in a region of direct binaural audition ; 
360-48 3 ef mixed 


Py) 7} 
and 26 i i indirect 


oP) 7) 


giving the necessary sum of 360 degrees. 3 
The angle @ differs naturally in different individuals, and 

has been diminished particularly in the female sex by the 

effect of the head-dresses worn for a long period. That this 


operates prejudicially on the hearing, at least in so far as it 


diminishes the extent of the direct binaural audition, may be 
inferred from what has already been said. It will be in the 
sequel more narrowly examined. It is self-evident that the 
range both of the direct and of the indirect monaural audition 
extends to 180 degrees. 

If the front part of the head is to offer to the sound-rays on 
their way to the ears no obstacle of such a nature as to di- 


EZ 


184 Prof. A. Steinhauser on the Theory 


minish their quantity, it will be necessary that the pinne of 
the ears should form tangent planes to the sides of the head. 
This is in reality approximately the case. 

Further, to fulfil the condition that no sound coming from 
the front shall be heard indirectly only, it is necessary that the 
surfaces of the pinne of the ears should not, when produced, 
intersect in front of the apex of the nose, n (figure 1) ; for 
in that case no sound-ray proceeding from the space included 
between the produced surfaces and the face could enter either 
ear directly. 

Hivery portion of the pinnz which reflects into the auditory 
meatus a sound-ray that falls upon it may be called, with re- 
spect to the direction of this sound-ray, an effective element of 
the pinna. The sum of all the effective elements for sound- 
rays in any given direction constitutes, for that direction, the 
effective surface of the pinna. 

The effective surface of the pinna is consequently different 
for every different direction of sound-rays. Also the intensity 
with which the sound is perceived depends upon the magni- 
tude of the effective surface. If then, as is found to be the 
case, the intensity of the sensation of sound be not essen- 
tially, or even disproportionately changed by a turn of the 
head (which in effect is equivalent to a change in direction 
of the sound-rays), it follows that the magnitude of the effec- 
tive surface must be nearly equal for all possible directions of 
sound-rays. 

The pinna therefore fulfils a special service as a reflecting 
curved surface ; and it might be possible, if time allowed of a 
protracted and attentive study of the point, to discover the 
particular purpose of each of its portions, and to discover its 
normal form. 

In its essential construction the pinna of the human ear 
consists of a funnel to collect the sound, and a reflector. The 
former, a (figure 2), serves to take up the sound-rays that 
come from the side, and behind ; the latter, b, to reflect those 
rays which come from the front, and also from the side, this 
reflexion being frequently accomplished with the aid of the 
rim of the ear S, as figure 2 also shows. 

Before turning to the theory of binaural audition, the ques- 
tion might be discussed why a man possesses two ears. For 
this fact, the following reasons might be assigned :-— 

First, the law of symmetry. This reason, however, is open 
to exception, since a single organ of hearing situated on the 
axis of symmetry of the body would not destroy its sym- 
metry. 

Secondly. The beneficial provision of nature which endows 


of Binaural Audition. 185 


man with organs in reserve. This ground is also not un- 
assailable, since indeed it is nature which permits mankind to be 
overtaken by disease which, on account of the close connexion 
between the double organ, almost invariably attacks both or- 
gans. So, usually, blindness attacks both eyes, deafness both 
ears, excepting always the comparatively few cases in which 
the imprudence of men, or accident, has destroyed one of the 
two similar organs. 

Thirdly. A certain faculty, perhaps, which man acquires 
from the possession of two ears, and therefore by hearing with 
two ears. We arrive at the conjecture that this may be the case 
by bringing into comparison two analogous facts in acoustics 
and optics :—that, in many cases at least, the place in which 
the source of sound is situated may be tolerably correctly 
judged of from the sensation of the sound ; and that man ac- 
quires a special faculty by the possession of two eyes, which, 
as is known, affords him a perception of distance. 

Now it will be shown in the sequel, that the power which 
man acquires in certain cases by hearing with two ears, con- 
sists in the faculty of discriminating the direction in which the 
source of sound is situated. | 

On the other hand, the distance of the source of sound can 
only be estimated approximately from the relative intensity of 
the sensation of sound, if the source of sound be known; for 
then the distance at which the source of sound is situated can 
be empirically determined from the difference between the 
perceived intensity and the known absolute intensity, or that 
which the source of sound would have in the immediate 
neighbourhood. In this manner, the distance of an enemy is — 
inferred in warfare from the intensity of the cannonading, 
or the distance of a carriage from the loudness of its rum- 
bling. 

It has been shown that we may distinguish between direct, 
indirect, and mixed binaural audition ; the next branch of our 
subject is therefore the theory of direct binaural audition. 


1. The Theory of Direct Binaural Audition. 


1. Let AA’ be the direction of vision, or line of sight ; ab 
and ac (or f; and /,) the effective surfaces of the two pinne 
for the (approximately) parallel rays of sound 8, @ the 
angle which these rays make with the line of sight, and 6 
the angle between the surfaces of the pinne and the line of 
sight. Then, if de is perpendicular to 8, ad (=m) measures 
the number of sound-rays which reach the left ear, and ae the 
number of sound-rays which reach the right ear. 


186 Prof. A. Steinhauser on the Theory 


We have then :— 
m = f, sin (2+ 8), 
n = ff, sin (B—@) 5 
consequently if, as is previously admitted, ,{=/2=/, we have - 
the equation 7 
m _ sin (2+ 8) 
| nm sin(@—a%) — 
Developing the sines 
m __ sinacosB+cosasinB | 
n  sinBcosa—cos#sin a’ 
and dividing numerator and denominator of right-hand mem- 


ber by cos acos B, 
m _ tan a+tanB. 


n  tanB—tana’ 
from which we may further obtain 
m+n _ tanB, 
m—n tang 


whence m—n 
Cam Som ene 2. OR Seay 


Further, let 7, and 2, be the intensities with which the sound 
which comes in the direction 8 is perceived in the left and 
right ears respectively ; then the principal considerations are 
expressed in the following equations :— 


m 1y 
nr Ie : 
and M—N — y—4y 


Mtn Wie 
Substituting this expression in equation (1), we obtain 


area) 
ae tan'p > 2 Se aes 
from which observe that the direction in which a source of 
sound is situated may be estumated by the different intensities with 
which a sound is perceived m the two ears. 

That which is here deduced from calculation our ears ac- 
quire by practice in the course of time. ‘That practice is ac- 
quired in the following way :—The first lesson which the ear 
learns, using the eye continually as its instructor, is to dis- 
tinguish the different kinds of sources of sound, as, for example, 
the clattering wagon, the clanking chain, the barking dog, &e., 
Conversely the ear thereby acquires the power of recognizing 
the source of sound, from the nature of the sound-wave. That 


tan C= 


of Binaural Audition. | 187 


source, as in the preceding examples of the wagon, the chain, 
&e., will therefore be looked out for by the eyes alone only so 
long as the power of drawing a judgment as to the direction 
is lacking to the ear. From the impressions which the sound 
coming in a direction now known makes upon the ears, the ears 
learn at last to recognize the direction in which the source of 
sound is situated, without needing the further assistance of 
the eyes. Thus every.one always looks for the source of sound 
straight in front in the line of sight whenever the impressions 
on both ears possess equal intensity. A coincident result 
may be deduced from equation (2), in which if 7,=7, we have 
tan a=0, and hence e=0. 

If, however, the effective surface of one of the two pinnz be 
artificially enlarged by holding the hollow of the hand behind the 
ear, and the intensity with which that ear perceives the sound 
be consequently increased, the source of sound, even if it does 
not change its real position, appears to move back toward 
that side on which the pinne has thus been enlarged. 

Suppose, for example, that, where originally ij=%, by the 
enlargement of the effective surface of the left pinne i be- 
comes greater than 7, Then in equation (2) the values of the 
: = ,and therefore also the value of tan a 

2 
and of the angle a, become greater than they were- before ; 
and the direction which is conjecturally assigned to the source 
of sound is moved on toward the left. 

Also by plugging one of the two ears more or less thoroughly 
with cotton-wool, an apparent change of direction in the source 
of sound can be brought about. - 

In all these investigations the eyes must be kept closed, in 
order that the judgment may not prejudice the illusion. A 
point of importance in complete coincidence with the fore- 
going observations is the phenomenon that individuals who do 
not hear equally well with both ears, always look for the source 
of sound more toward that side on which the ear of better 
hearing is situated. Thus if the worse-hearing ear is the left 
one, and it perceives a sound of intensity 7, with only the mth 
part of that intensity, then 


(proper) fraction 


188 Prof. A. Steinhauser on the Theory 


Now the fraction — 
u— ta 
% 

Soult be if both ears heard equally well. Consequently the 
direction in which the source of sound appears to be moves 
towards the right, or towards that side on which the ear of 
better hearing is situated. In tne case of a complete deafness 


ee is in all cases less than the fraction 


; hence also tan a and the angle a become less than they 


ofone earm= o; hence tana = a . tan B = tan 6, andi 


— (3, where the negative angle is fo. be reckoned on the right 
of the line of sight. 

2. Let two consonant tones be produced by organ-pipes (in 
the apparatus to be described below, which I call a homo- 
phone, and which is for the ears the analogue of the stereo- 
scope for the eyes), but in such a manner that one tone, 
having the intensity 7,, shall affect the left ear only, and the 
other tone having the intensity 7 shall affect only the right 
ear; then, at least when the eyes are closed, the two impressions 
unite in a single impression which appears to be produced 
by a source of sound in the direction a as determined by 
pdpation (2) :— ; 

an a 


. tan p. 
=a i 
This apparatus is shown in plan in figure 4; where abc re- 
presents a wooden tube of square cross section, closed ata and 
c, and provided at 6 with a mouthpiece through which a con- 
tinuous blast of air from a bellows may be introduced. Near 
the ends a and c, two flute organ-pipes, p; and po, are inserted 
into two holes in the tube. ‘The pitch of these pipes is alike ; 
but the relative intensities of their tones can be brought to any 
desired proportion by means of the valves m and n, which re- 
gulate the current of air. The cardboard funnels T, and T, 
respectively lead the tones to the ears O, and O, of the observer 
whose head is represented at K. 
3. Suppose two persons, A and B, for whom the values of 
6 differ, to make an estimation of the direction of a sound 
under precisely similar conditions, and that in both cases, 
therefore, the sound-rays and the line of sight include the angle 
as agreeably with that which has preceded, the measurements 
for reckoning the sound-rays which respectively enter the left 
and right ears for the two observers will be 
A. m=/fsin («+ 8,) 
and ny =fsin (8,—a@); 
B. m,=fsin (@+ Be) 
and Ny =f sin (G,—«). 


of Binaural Audition. 189 


Now, in order to learn whether in the case of a single sen- 
sation of sound the ratio between the intensities of the sensations 
in the two ears is the same for both individuals, we have ob- 
viously only to determine whether 


or whether 
sin(a+,;)__ sin(a+ ,) 
sin(@;—«) sin (@,;—2)’ 


since, according to what has already preceded, those intensi- 
ties are in the proportion of each m to its respective n. 
Developing the sines, we get 


sinacos§,+cosasin§; _ sinecos®,+cos asin By 
sin 8, cosa—cos sina sin 8,cosa—cos sina 


Hence, by algebraic proportion, 


2eosaesin 8, 2cosasin BP, 
a Eo a = SS ae 
2sineacosB, 2sinzecosP, 


sin 6; _ sin B2 
cos, cos By. 


tan 8,= tan B., 


which can only be true in the case proposed if B,=/.. 

The premised condition, that the ratio between the intensi- 
ties with which the two ears of an observer perceive a sound 
is the same for two observers for whom the angle 8 differs 
while other conditions remain the same, is therefore inexact ; 
whence the standard of each individual for the perception of the 
direction of sounds is dependent upon the angle B included be- 
tween the effective surfaces of the pinne of his ears. Suppose, 
for example, that in the observer A, 6,;=25°, and in the ob- 
server B, 8,=30°, and that the angle « which the sound-rays 
make with the line of sight of each of the observers is 30° ; 
then :— 


whence 


For observer A: 
m=fsin («+ B,)=/sin 45°, 
ny =f sin (6,;—e)=/sin 5° ; 

consequently the ratio of the intensities is 


m,: y= sin 45° : sin d°=0°707 : 0087 =81: 1. 


190 Prot. Ac Steinhauser on the Theory 


For observer B: 
m,=/ sin (« + B.)=/fsin 50°, 
Ng =f sin (C,.—a)=/sin 10° ; 
consequently the ratio of the intensities is 
My? N= sin 50°: sin 10°=0°766 : 0173 =44 = 1, 


The source of sound will therefore be sought for by observer 
A in a direction 20 degrees to the left of the line of sight when 
the intensity of the sensation of sound in the left ear is more ~ 
than eight times as great as that of the sensation in the right . 
ear, but by the observer B when the intensity of the sensa- 
tion in the left ear is not quite 43 times as great as that in the 
right ear. 

I think, then, I may not inaccurately conclude that the per- 
ception of the direction becomes the more certain as the differ- 
ence between the intensities of the sensations of sound in the 
left and right ears is the greater—just as analogously the dis- 
tance of a body may be the more surely estimated in binocular 
vision the smaller that distance is, or as the directions of the 
two optic axes differ more and more widely. 

The difference between the two intensities will, under similar 
conditions, be greatest for that individual for whom the differ- 
ence m—n has the greatest value. And since 


m—n=f sin (a+ 8)—fsin (8B—«) 
=/ (sin « cos 8+cos «sin 8B— sin 8 cos a+ cos # sin @) 
= 2/sin « cos B, 


this value becomes greater as cos 8 becomes greater, or as 
angle 8 itself becomes less ; consequently the smaller the angle 
included between the line of sight and the surfaces of the pinnae, 
the more certain will be the perception of the direction of sounds. 

4, We are now prepared to pursue the investigation of the 
direction of best hearing, 1. e. of the direction in which a source 
of sound at a given distance must be situated in order that it 
may be heard or perceived best. 

Hearing is obviously better in proportion as the rays of 
sound which reach the ears from the source of sound at the 
given distance are more numerous, or as the dimensions m 
and n of figure 3 are the greater. Hearing with the two ears 
will therefore be best produced when the value of the sum 
m+n is greatest. Now it was shown that 


mM =f sin (a +8) =/ (sin & COS B + Cos a sin 8), 
n=/fsin (@—«#) =f (sin 8 cos a—cos 8 sin @) ; 


ee 


of Binaural Audition. 191 
therefore (m+n) will be a maximum when 


f(sine cos 8+cos asin 8+sin 8 cosa—cos A sine), 
or 
| 2fsin B cos « 


isamaximum. But in this expression, so long as one person 
only is concerned, the only variable is a; consequently 
27sin B cose will have its maximum value, namely 2/sin 8, 
when cos @ is a maximum, which occurs when «=0°. 

We hear best therefore with the two ears when the sound reaches 
us from the front in the line of sight. 

It is in consequence of this that we always turn with our 
face to the speaker, provided that we possess equally good 
hearing of the two ears. 

If this be not the case, .and we hear worse (for example) 
with the right ear than with the left, and to such an extent 
that we perceive a sound of intensity 7, with only the xth part 
of that intensity, then to find the direction of best binaural 
audition the problem will be the same as if the right ear were 


considered to receive only = rays of sound instead of n rays, 
or as if the effective surface of that ear were not f but 
only l . Proceeding on this assumption, we see at once that 
if, in figure 5, ab=/, and ac= = the straight line de drawn 
at right angles to the direction of the rays of sound S measures 
the sum of the rays of sound which reach both ears, and that 
this straight line is longest when parallel to be. The best 
binaural hearing therefore occurs when the direction of the 
rays of sound is perpendicular to the straight line be. In 
order to find the angle a, which gives the direction of best 


hearing for the case under discussion, we have only to consider 
that, in figure 5, be=cd, also that 


be=/ cos («+ B) 


or 
=f cos «cos B—f sin « cos B, 
and that 
cd= f (cos (6 —a) 
or 
=" cos B cosa + T sin B sin a : 
whence 


fcosa«cos B—/sin « cos B= L cos cos att sin B sine. 


192 Prof. A. Steinhauser on the Theory 
From which it follows that 
x cos a cos B—wsin «sin B= cos B cos a+sin B sina, 
and, further, that 
(2—1) cos acos B=(x +1) sin asin B, 
whence by algebraic transformation, 


tang imma 
rere 


Tan a and also angle « increase in value as the proper frac- 


cot . 


tion aes increases ; but this fraction becomes greater as x 
increases in value, and w increases as the degree of deafness 
of one ear increases. It follows, therefore, that the person hard 
of hearing must, in order to hear best, turn to the speaker 
his better-hearing ear to a larger degree in proportion as the 
hearing of the other ear is relatively worse. 

In the case of complete deafness of one ear, c= , and our 
formula becomes 


= 
tan «= i cot B, 
ie 
2 
or 
tan a =cot B, 
whence 
a=90—B, 


which is the case when the rays of sound are perpendicular 
to the surface of the hearing ear, and that ear is turned straight 
towards the speaker. 

In the case of two different individuals the angle ( is gene- 
rally different. Suppose two individuals hard of hearing in 
one ear to an equal degree. Since tane and angle @ are 
greater in proportion as cot 8 is greater and as ( is less, it fol- 
lows that persons equally hard of hearing in one ear must, in 
order to hear as well as possible, turn the better-hearing ear 
the more towards the speaker in proportion as the angle which 
the surfaces of their pinnee make with the line of sight is less. 
The cases of hardness of hearing in both ears may be separated 
into two: (1) the cases in which the two ears are equally hard 
of hearing ; (2) the cases in which they are unequally hard 
of hearing. 

In the jirst case suppose, for example, that the left ear 


of Binaural Audition. 193 


hears only with intensity - instead of intensity 7, and the right 
ear with intensity = instead of intensity iz The direction in 


which the source of sound is estimated to be situated is, in 
accordance with our preceding paragraphs, given by the 
equation 


4 Ie 

x 

tane= -= = 
1 2 

oS + — 

ie ee 


which cancels into 
4 —t9 
tan e= AT tan 6. 

But since this equation gives the same angle which was found 
when both ears possessed normal hearing powers, it follows 
that the power of perception of the direction of a sound ts not 
vitiated by an equal hardness of hearing of both ears. This is 
indeed reasonable on other grounds, since the distance of the 
source of sound on which the intensities of the two sensations 
is dependent, but of which the ratio between those intensities 
is independent, exercises no influence on the perception of the 
direction. | 

The second case may obviously be referred to cases already 
treated in detail, if we make the supposition that we may take 
the “effective surfaces’? of magnitudes proportional to the 
respective powers of the two ears. 

Best hearing with one ear must obviously occur when 
m=fsin (a+) becomes a maximum, which, since 6 remains 
constant for a single individual, will occur when sin (2+/)=1, 
or when (2+(6)=90°, or, finally, when 2=90°— 6. This 
agrees with figure 3, if the direction of the rays of sound be 
made perpendicular to the surface of the pinna /,, in which 
case m=f,=/. 

Finally, let us consider that the greatest number of rays of 
sound which can be received by both ears is measured, accord- 
ing to what has been established early in § 4, by the expres- 
sion 2/sin 6, in which case the source of sound is situated in 
the line of sight; further, that the greatest number of rays of 
sound which can be received by one ear is measured bv /, in 
which case the ear in question is turned towards the source of 
sound. Hence it follows that, assuming the specified positions 
of best hearing, the hearer will hear better with one ear than 
with both ears, if in his case 


f> sin B. 


194 Prof. A. Steinhauser on the Theory 


But if this is so, 
| 1>2 sin B, 
or 
£>sin B; 
and in this case, 
B2our 

Now, since it is the fact that for most persons B<30°, this 
explains the well-known position assumed by the listener who 
turns one ear towards the source of sound. | 

5. In the theory of Binaural Audition developed in the pre- 
ceding paragraphs, it has been tacitly assumed throughout 
that the source of sound should be situated in that plane (usu- 
ally horizontal) in which the line of sight and the line joining 
the middle points of the two pinne are situated. This is not, 
however, always the case; for while the line of sight may be 
horizontal, the source of sound may be situated above or below 
the imaginary horizontal plane. Hence it is necessary to 
enlarge the theory of binaural audition in this respect. In 
figure 6, which is drawn in so-called parallel perspective, let 
A A’ be the horizontal line of sight; then fy or adge, and /; 
or adeb are the effective surfaces of the pinne, each enclo- 
sing the angle 6 between it and the line of sight. Let the 
plane dk be a prolongation of one of these planes, f,. Lastly, 
let a M be the direction of any ray of sound (the position being 
a general one) whose projections are M’a upon the vertical 
plane dk, and M’a upon the horizontal plane ag. Then to 
reckon the rays of sound (assumed parallel to one another) 
which meet the surfaces f; and /, in the given direction de- 
fined now by the angle y vertically, and by the angle e hori- 
zontally, we must take as measures of the number of those 
rays the cross sections which can be led orthogonally through 
the two quadrangular prisms which have respectively for their 
bases the surfaces /, and /,, and whose long edges are parallel 
to the direction of the rays of sound a M. 

These cross sections, which may be drawn upon one common 
plane perpendicular to the direction of the rays of sound, may 
be regarded as the projections of the surfaces /; and f, upon 
that plane. And since the area of the projection of a plane 
figure is equal to the product of the area of that figure into 
the cosine of the angle included between the plane of the figure 
and the plane of projection, we shall be able to find the areas 
of the cross sections, provided we first know the angles w, and 
w, Which the direction of the rays of sound makes with the 
surfaces f; and f, respectively. Now the plane taken normally 
to the direction of the rays of sound is the plane in which the 


of Binaural Audition. 195 


cross sections are situated. Let us call the angles included 
between that plane and the surfaces f; and /2 respectively ¢, 
and d,. We know also that 90°—w,=¢y, and 90°—we=¢e3 
and hence the areas of the cross sections 7”; and /’, are respec- 
tively f; cos dy, and f, cos do. 

The remainder of the calculation follows the course thus in- 
dicated. From figure 6 we learn that 


MM”=WMW’n=aM sin wz, 


M’n 


aM.” 


and sIn W.= 


Further, since angle A’an=8, 


M’n=aM sin (G—a@). 


But 
a aM 

cos y 
whence 

aM’ sin (@—«) 

sin WW, = aM’ : 
cos ¥ 

and 


sin w,= sin (B—«a) cos ¥. 


Here wy is the angle included between the direction of the 
rays of sound and the surface /,, since that angle is, as we 
know, also the angle which that direction includes with the 
projection of the surface /5. 

Now imagine the surface /, rotated about the straight line 
ad to the right until the line ac forms a continuation of ba. 
The angle 8 which this surface included with the line of sight 
is thereby changed into the angle (180 — 6), while the surface /Z 
has changed into the position of. the surface f;. Hence, in 
order to find the angle w,, which is included between the 
direction of the rays of sound and the surface /;, we have 
merely to replace 6 in the preceding formulse by the value 
(sof). 

We have therefore 


sin w,= sin [180°—B—a] COS Y; 
= sin (e+) cosy. 


Let $, and ¢, be the angles which are respectively included 
between the surfaces 7; and /, and the plane which we have 
taken normally to the direction of the rays of sound; then, 


196 Prof. A. Steinhauser on the Theory 
since ¢,=90°—w,, and $2= 90° —we, we have 


cos $;= sin w,= sin (2+) cosy, 
COS ho= Sin We= sin (B—«) cosy; 


and the areas of the cross sections of the parallel pencils of rays 
of sound which reach the left and right pinne, respectively, 
are 

Ji=/fi cos d1=f; sin («+ B) cos y, 

fo=fr00s $y=fysin (@—a) 008 y. 

But as these cross sections constitute, as has already been 
shown, the measures by which the rays of sound which respec- 
tively reach the left and right pinne are to be reckoned, we 
may draw the following conclusions :— 

(1) That, with respect to the angle of altitude y, the chailer 
this angle becomes the better will the hearing be, since in the 
sum 

ti tfe=fi sin (2+ 8) cos y+/2 sin (8—«) cos y, 
which must be a maximum for the condition of best hearing, 
both terms have maximum value when y=0. 

We hear therefore binaurally the best, relatively, when the 
source of sound is situated in that plane im which are 
situated the line of sight and the line joining the middle points 
of the pinne (“ plane of best hearing’’), and the best, absolutely, 
when it rs situated in the line of sight. 

(2) That the intensities 7, and 7, with which a sound is per- 
ceived in the two ears, for any values of y whatever, always 
remain equal so long as «=0, since then 


fi=/.isin B cos y=f2 sin B cos y, 
and, because /;,=fo=/, 
fi=/ sin B cos y, and f',=/sin 6 cos y. 
(3) That the intensities 7’; and 7, with which a sound 


coming from above or below (in the latter case y is negative) 
is perceived in the two ears, are in the ratio 7; :f’s, or as 


sin («+ ): sin (@—a). 
And since also in this case the proportion 
41: ig= sin (2+ 8) :sin (B—«a) 
holds good, which was deduced for the case in which the source 


of sound was situated in the plane of best hearing, it follows, 
either by calculation from oe (2), that 


ba ee ee te gern Bs 
‘i 


of Binaural Audition. » 197 


or by what we know from practical experience, that in the case 
of hearing a sound coming from above or below, we are able to 
estimate, from the relative intensities with which the sound 1s 
perceived in the two ears, the azimuth of the rays of sound as 
projected upon the plane of best hearing. 

This explains the method which we pursue to discover the 
position of a source of sound whose situation is unknown, and 
which consists in a motion of the head. 

For example, to find a source of sound situated anywhere 
above, we have only to turn the head about a vertical axis until 
we hear equally with both ears and with the greatest total in- 
tensity. Then the line of sight coincides with the horizontal 
projection of the direction of the sound. The head must then 
be turned upwards about a horizontal axis at right angles to 
the line of sight, as long as the intensity of the sensation 
increases. 

When this reaches its maximum, and is equally great for 
both ears, then the source of sound must be situated in the 
line of sight. 

And here we must remark on the essential importance of 
the actual conditions—that the ears and eyes, being alike at- 
tached to the head, share its movements, and that they are 
situated at almost the same height above the ground. 

Should we perceive a falling-off in the intensity of the 
sound on raising the head, this would be an indication that 
the source of sound is situated below the plane of best hearing, 
and that we should be able by sinking the head to bring the 
source of sound into the line of sight in the manner just de- 
scribed for a sound above the head. 

It is intelligible and natural that, where (as in an instrument 
for measuring altitude and azimuth) we have two separate 
motions of rotation at right angles to one another, it is imma- 
terial whether the movements in the two directions be executed 
separately or by a simultaneous motion of the head. 

This occurs, for example, when we try to find a lark which 
we may hear singing above a field. We raise the head, 
making an arbitrary guess at the position of the lark in the 
sky. Then we turn the head about, led meanwhile by ear 
until we hear equally well with the two ears and with the 
greatest possible intensity; and simultaneously we perceive 
the lark in the line of sight. We do not, therefore, as it might 
be conjectured in this case, seek for the source of sound by 
means of the eyes, but by means of the ears. 


[To be continued. | 


Phil. Mag. 8. 5. Vol. 7. No. 42. March 1879. Q 


E-198...] 


XXXIV. On the Determination of the Variation of the Thermal 
Conductivity of Metals with Temperature, by means of the 
permanent Curve of Temperature along a uniform thin Rod 
heated at one end. By Outver J. Lover, D.Se., Lecturer 
on Applied Mathematics and Mechanics at University College, 
London*. 
[Plate X.] 


1; he approximate theory of the flow of heat down a 

uniform rod heated at one end and exposed to cooling 
influences everywhere else was, I believe, given by Biot before 
the time of Fourier, and was also verified experimentally by 
him. The “constants’’ occurring in Biot’s equation to the 
curve of temperature have long been known to be variable ; 
and numerous experiments have been made to determine em- 
pirically in what manner they depend upon the temperature. 
Nevertheless Biot’s method in its original form has been fre- 
quently employed by subsequent observers in order to compare 
the conductivities of different metals—by Ingenhousz for in- 
stance, by Despretz, and even in the far more accurate expe- 
riments of Professors Wiedemann and Franz. Principal 
Forbes, on the other hand, devised and executed a method 
which was quite independent of any equations to curves ex- 
cept those deduced from experiment; and by graphical and 
ether laborious methods he determined both the absolute con- 
ductivity of wrought iron and its variation with temperature. 
But, as far as I know, no recalculation of the curve of tempe- 
rature with the improved data now accessible has been made. 
It therefore seemed worth while to obtain as close an approxi- 
mation to the equation of the true curve of temperature as is 
practicable without cumbrous integration, and to see how far 
the improvement affects the results of those experimenters 
who, unlike Forbes, depended on the theoretical curve of tem- 
perature. Moreover it seemed probable that the more accu- 
rate equation to the curve would enable the variation in con- 
ductivity of the rod with temperature to be calculated in some 
moderately simple manner, and with far less labour than that 
gone through by Forbes. Forbes’s methods are perfect; the 
only objection to them is the excessive tediousness of the pro- 
cess of discussing the experimental results. And as it is a most 
important research at the present time to compare exactly the 
law of variation of thermal and electrical conductivity in the 
same piece of material, it seemed desirable to have some means 
of calculating the law of thermal variation from some simple 


* Communicated by the Physical Society, an abstract having been read 
on the 8th of February, 1879. 


On Variation of Thermal Conductivity of Metals. 199 


experimental data ; and the long-thin-rod form of experiment 
is evidently suitable for observing the variation of electric con- 
ductivity with temperature. 

The following paper is unfortunately rather long; but the 
length is due to the necessity of fully discussing experimental 
results, and I have skipped nearly all the mathematical steps, 
as they are elementary and of no interest. 

2. Consider a thin uniform infinitely long rod, of perimeter 
p and cross section g, made of a material whose specific con- 
ductivity is k, density p, and specific heat c. Let this rod be 
surrounded by an enclosure at the absolute temperature vp, 
and let one point of the rod (which we will call the origin) be 
kept by some means at a constant temperature © above that 
of the enclosure ; then heat will flow from this point along the 
rod and will be dissipated at its surface, and the temperature 
of every point of the rod will rise at a rate proportional to the 
excess of the quantity of heat which it gains per second by 
conduction, over that which is dissipated by radiation and con- 
vection. After a long time, however, this excess of heat 
vanishes, and the temperature of any point of the rod ceases to 
rise, having attained a constant temperature 0 above that of 
the enclosure—its absolute temperature, ¢, being therefore 
O+v,. (I willadhere to the letter v for temperatures reckoned 
in Centigrade degrees from absolute zero, aud to @ for tempera- 
tures reckoned from the temperature of the enclosure as zero. 
We shall have to use occasionally the Centigrade zero—the 
temperature of melting ice ; and temperatures reckoned from 
it may be denoted by ¢.) 

The heat which flows in unit time past any cross section of 
the rod at a distance x from the origin will be 

dé 
Kg dx” 
and the gain of heat per second by an element of volume gd 
in this position will be the differential of this quantity, or 
dé 
kad ie 
If every unit area of the surface of the rod at this point is 
losing by radiation and convection the quantity H per second, 
the rate of loss of heat by the surface of the element is 
Hpda, . 
the product pda being the area of its surface. As long as the 
temperature of the element is rising, the rate of rise of tempe- 
rature will be the difference of the last two expressions divided 
by the thermal capacity of the element—that is, divided by 
Q2 


200 Dr. O. J. Lodge on the Variation of the Thermal 


cpgdz; but when the permanent state is reached, the heat 
gained and the heat lost become equal, and their equality is 
the fundamental differential equation for the permanent state 
of a rod, viz. 


do 
kad aaet Hopdz, 
or 
#0 _ Up 


dx’ kg° * ° ° a) 6 . e (1) 


The four quantities which enter into the right-hand side of this 
equation are all variables, and may be expressed as functions 
of @. It has, however, been always assumed, in the approxi- 
mate theory hitherto used, that H is the only variable, and 
that it is simply proportional to the excess of temperature, and 
can be written 


E90, 


where f is a constant. (This is called Newton’slaw.) What 
we now want to do, however, is to take into account the vari- 
ability of all these constants as far as present experimental 
results will enable us to do so, and then to integrate the above 
equation to as great a degree of accuracy as is easily possible. 

3. Now, if an isolated body of volume V, surface 8, density 
D, and specific heat C loses from each unit of surface a quan- 
tity of heat H per second, then its rate of fall of temperature 


is 
by dv a el Sites 
dt os VDC? 
writing » or6 for the essentially positive quantity — 2 Hence 


dt 
an element of the rod (§ 2), if isolated from its neighbours by 
two flat impervious films, will cool at the rate 
AS Hpda 
cp dx 


whence its rate of loss of heat per unit of surface is 
oo Bee 
oe aes 3 ees 


Substituting this value of H in equation (1), it becomes 
oa 26 @) 
app 4 

which is precisely the form of the equation to the variable 

flow of heat through a slab*, though 6 has there a very diffe- 


* See Everett, Trans. Roy. Soc. Edinb. vol. xxii. 


Conductivity of Metals with Temperature. 201 


rent meaning. ‘The product cp is the capacity for heat of unit 
volume of the rod (p being the mass of unit volume) ; hence 


E is the conductivity in terms of a unit of heat which can 
p 


raise unit volume of the rod one degree. This Professor Max- 
well calls the thermometric conductivity*, as distinguished 
from the calorimetric conductivity k. 


4. In equation (3), @ is a function of 6; andif the element 
were not supplied with heat, it would cool at the rate 0, and 


both @ and 6 would be functions of the time. But when heat 
is supplied to the element at a compensating rate by its neigh- 


bours, @ is constant, and therefore also @ is constant as regards 
time; yetstill the rod will emit heat at the same rate Has before, 
and @ will be the same function of @ as if it were actually 
cooling : hence 6 was called by Forbes the statical rate of 
cooling. 

The relation between 6 and @ for a cooling body, or the 


curve which expresses 0 as a function of 0, has been investi- 
gated experimentally by Dulong and Petit, and found to be of 
an exponential form. Newton’s law made it a straight line. 
Forbes called it the secondary curve of cooling, and found a 
point of inflection on it for a long body cooling in air. For 
a rod ina permanent state, 0 is a function of w; and the curve 
0, x is the statical curve of temperature down the rod, and is the 
one we want to investigate. The curve 6, x is what Forbes called 
the statical curve of cooling. Finally, the curve expressing 0 
as a function of time is the ordinary curve of cooling of a 
body. The general nature of these last three curves is the 
same, and depends on that of the first curve 0, @. The first 
rough approximation to them is that they are all logarithmic, 
this being a consequence of the hypothesis that the first curve 


is a straight line. I suppose that the fact that @ is only appa- 
rently a function of the time renders abortive the analogy be- 
tween equation (3) and the equation to the variable flow of 
heat in a slab. 


On the Variation of with Temperature as at present known. 


5. Professor Tait has given theoretical reasons for assuming 
the conductivity (7. e. the thermometric conductivity) of every 
substance to be inversely proportional to the absolute tempe- 
raturet; but I do not know whether he lays much stress upon . 


* See Maxwell’s ‘Theory of Heat,’ p. 235. 
See ‘ Recent Advances,’ p. 271. 


202 ~=9Dr. O. J. Lodge on the Variation of the Thermal 


the correctness of the theory. At any rate it does not seem 
to agree very well with the results of experiment, except in 
the case of iron. The experiments of Principal Forbes* estab- 
lished the fact that the thermometric conductivity of wrought 
iron is nearly inversely proportional to the absolute tempera- 


ture; but the agreement is not quite perfect, as the following 
Table shows. 


Conductivity 
at the temp. | Product of 


. ¢, as found | conductivity Produce 
Centigrade iter Ges ok Scere ake nearly| Product, 
tempera- y coe constant, k 
4s reduced to | vemperature, | (308-a 
ture, C.G.S. units, k | (400+0 & co 
k (27442) a cp 
co. 
i 2331 63:87 93-24 72-26 
50 "1995 64:65 89°78 71°82 
100 "1764 65°98 88°20 72°32 
150 1629 69-08 89:60 74:93 
2 J "1528 72°41 91°68. 
250 "1440 75°43 93°60 


The third column contains the numbers which ought to be 
coristant if the theory were accurate. The fourth column con- 
tains numbers calculated on the hypothesis that the conducti- 
vity varies inversely as the absolute temperature increased by 
some constant, say by 126. ‘These numbers agree with one 
another rather better than those in the preceding column; 
but still there is a regular divergence perceptible between the 
hypothesis and the experimental results, especially at high 
temperatures. 

The results at the higher temperatures, however, do not 
seem to have been regarded by Principal Forbes as equally 
dependable; for he gives an empirical formula for the con- 
ductivity at any Centigrade temperature ¢ which does not 
agree very closely with the experimental results at high tem- 
peratures, saying, “ I have assumed that the most trustworthy 
part of the observational curves are those between the actual 
temperatures of 40° and 160°, and that within moderate limits 
the conductivity may be represented in terms of the tempera- 
ture by such a formula as ”’ 

& =A+Bi+C?, 
cp . 


* Trans, Roy. Soc. Edinb. vols. xxiii, & xxiv. 


Conductivity of Metals with Temperature. 208 
where the constants for the best of his two bars, when reduced 
to the O.G.8. system, are 

A=*2331, B=—-:00755, C=-00000189. 


6. Forbes’s formula may therefore be written 
iE a -2331(1—-00324¢ + 00000812); 


and this may be very accurately expressed by a form more 
suitable for our present purpose, ate For this last may be 


regarded as the sum of an infinite geometrical progression with 


ratio — a and may be without approximation, - 


Bf gf) 
— 2) Ghee, 
stopping at any term one “i and multiplying it by a 


instead of writing the remaining terms. 

Now it T be the highest temperature to which the formula 
is required to apply, the average temperature $T may be in- 
troduced into the denominator of the last term instead of the 
variable ¢, without making much difference ; and the above 
may be written approximately, te at the third term, 

ie 44 G—$ yd 
b+t b- b Seeuy 


This expression agrees very well with Forbes’s formula for a 
range of 200°; for taking b6=308, T=100, and - = Zool, 
it becomes 
a 
308 +¢ 
Hence I shall assume that the results of Forbes may be 
summed up in the equation 


=°2331(1—-00325¢ + 0000082’). 


(4) -* = Ur ae (4) 
cp/ we 808+¢ 8084+¢ ap, = = ° 


The numbers in the last column of the preceding Table give 
the values of the “constant’’ A, for the temperatures consi- 
dered most trustworthy by Forbes, 

7. The variations of conductivity with temperature have 
also been investigated, by a method depending on fluctuating 


* The symbol -. is used merely to signify approximate equality. 


204 = Dr. O. J. Lodge on the Variation of the Thermal 


temperature, for copper and iron by Angstrém* ; and his 
result for iron, reduced to the C.G.S. scale, can be expressed 
in the following way, 


(=) ~=+2143(1—-0028740), ; 
CP’ Fe 
es A’ 
which may be considered as equivalent to 1a for a small 


range of temperature. 


The results of Angstrém for copper are summed up in the 
following formula, ) 
(=) —1-163(1—"0015192), 
cp Cu 
SBS a1 — when ¢ is small. 

8. The law of variation of the ordinary or calorimetric con- 
ductivity & can, of course, be deduced from the above by mul- 
tiplying them by the value of the product cp, with each of its 
factors expressed as a function of the temperature—the one 
factor from the experiments of Bede on specific heat, the other 
from the expansion experiments of Fizeau. This Professor 
W. Dumast has done. Using a mean coefficient of expansion 
between 0° and 100° C., he writes for the density of iron, 


p=l7T799(1 —:000036842) ; 


which may be expressed as 


and for its specific heat, 


c='1053(1 +:0013482). 
Multiplying Angstrém’s value of = for iron by the product of 
these two quantities, we obtain 


k=-1862(1—-001562). 


And multiplying Forbes’s numbers for o (nominally for 4), 


as reduced to the C.G.S. system by Dr. Everett, on page 44 
of his book on Units (first edition), by the variation factor 
(1+-001311¢), we obtain the real values of & at the different 
Centigrade temperatures ¢ according to Forbes’s experiments, 


Phil. Mag. vol. xxy. 1863. 
i bros: Ann, cxxix. See also Wiillner, Zxp. Physik, vol. iii. pp. 286 


Conductivity of Metals with Temperature. 205 


t ke 
(jpn eeereiers oitiseatepiatslelefe ois’ "207 
Daa Rita t de caic sees oeeewe ee “195 
DO tdiileas cosdsnsdacees 6 189 
(BG crc oteiece eo oer 182 
ROOM perar ss icnsenesacs cee. oY 
POU iemederine-io- cclnccaos ese af 


numbers which can be expressed with considerable accuracy 
by the formula 
k=:207(1—:00144¢). 

9. The result of all this appears, then, to be that, as far as 
experiment has hitherto gone, the conductivity (both calori- 
metric and thermometric) of the metals copper and iron may 
be expressed with moderate correctness as a linear function of 


the Centigrade temperature, with a negative value for a or 


Be Be 

ap 
and that it may be expressed with a trifle more accuracy by 
an inverse function of the temperature, 


ESE 
co b+ 0’ 
because this may be written very approximately, when 6 is 


much bigger than ¢, 
A (1 t ) 
pp pay 


I will therefore assume that the variation of conductivity in 
any metal for moderate ranges of temperature is expressed by 
the equation 
Acp 
k = BE? ° ° ° ° e .  e (4) 


and that, since the variations of density and specific heat are 
known, the law of variation of conductivity in different metals 
is sufficiently discovered as soon as we have found the value 
of the constant 6 for each metal. Our object then is to find a 
mode of calculating 0. 


On the Variation of 0 with Temperature. 
10. We have now to consider in what way the other factor 


of the right-hand side of equation (3), namely 6, may be ex- 
pressed as a function of the temperature. 
The magnificent researches of Dulong and Petit on this 


206 Dr. 0. J. Lodge on the Variation of the Thermal 


point have established the following expression for the velocity 
of cooling of a body whose absolute temperature is v, in an 
enclosure of absolute temperature v), containing gas at the 
pressure a, | 

= P(a’—a”) + Qas(v— ba 


' which may also be written in terms of the excess of tempera- 
ture 0=v—»,, thus, 3 


6=Par(a®—1)+Qaeor™, . . . . (5) 


The first term is the rate of cooling by radiation; the second 
term is the rate of cooling by convection. In other words, Q=0 
in a vacuum ; and P is small if the surface of the body is sil- 
vered, but great ifit be lampblacked. The constant g depends 
on the nature of the gas; for air itis ‘45; but a is said to be 
a universal constant, and equal to 1:0077. Although this is an 
empirical formula, it is perhaps the most perfect example of 
such a formula that we have, and it expresses Dulong’s results 
thoroughly well. ‘The necessity of such an elaborate expres- 
sion has been called in question by Narr; but his experiments, 
so far as they go, seem rather to confirm than to upset this ex- 
pression ; and it has been in the main verified by Provostaye 
and Desains. , 

11. Some caution, however, seems advisable with respect to 
the second term, which expresses the loss by convection as 
constant power of the excess of temperature; because it was 
found by Principal Forbes that when the excess of tempera- 
ture was very small, the loss by convection was almost inap- 
preciable; and he suggested the viscosity of the air to account 
for this—some finite excess of temperature being required to 
set convection-currents going. ‘The point of inflection, more- 


over, which Forbes found on the curve 0, @ at a high tempe- 
rature (see § 4) is wholly unaccounted for by Dulong’s expres- 
sion ; but it is probable that here the experiments of Dulong 
are the most accurate, and that the contrary flexure of Forbes’s 
curve was due to waves of heat in the elongated mass whose 
cooling he investigated*. Hxperiments on the rate of cooling 
of bodies at the ordinary pressure of the atmosphere have been 
made by Mr. Macfarlane and by Mr. Nichol; but their excesses 
of temperature only went as high as 60° (see Everett, ‘On 
C.G.S. Units,’ p. 50). Ibelieve ProfessorsAyrton and Perry 
have some results not yet published. 

On another ground also caution seems to be rendered ne- 
cessary by the kinetic theory of gases, as illustrated in the 


* Or see Professor Tait’s explanation given to the Royal Society of 
Edinburgh on the 20th of last January (‘ Nature,’ No, 486, p. 379). 


Conductivity of Metals with Temperature. 207 


experimental investigations of Mr. Crookes; for if the en- 
closure containing the cooling body be gradually exhausted 
of air, so that w progressively diminishes, a discontinuity, 
in the direction of a sudden increase in the rate of cooling, 
would probably arise at the instant when the average free 
path of the molecules was long enough to reach from the 
surface of the cooling body to that of the enclosure. And it 
is probable that for exhaustions higher than this the law of 
cooling is different, and in all probability simpler than it was 
when the heat had to be conveyed between the surfaces by 
the unsystematic and irregular agency of convection-currents, 
a process of true gaseous conduction then setting in. This is. 
_a point which should be attended to in subsequent investiga- 
tions ; and it would be an important though somewhat difficult 
research to discover experimentally the law of cooling and its 
alteration with pressure when the distance between the cooling 
body and enclosure is less than the free path of the molecules: 
probably it could be more readily deduced from theory. It is 
not likely, however, that any of the investigators on the law of 
cooling hitherto have attained an exhaustion any thing like so 
perfect as this. | 
12. These objections, however, only apply to the convection 
part of the formula (5); and I will assume that the radiation 
part 
Gorge lia Shao bse G2 (5) 


is practically true as it stands. Since this, however, is not a 
very simple function for a second differential coefficient like 
(3), it will be well to see with what amount of accuracy we 


may expand it into a series and neglect higher terms. The 
expansion 1s 


1 1 1 
é= Par(9 log a+ 5 (Blog a)? + 5 (Blog a)’ + 3; @loga)' +... :) (6) 


which may be conveniently written 
eee ea 2 5 ght Nleiges f 
d= flog 4): ae +6+ 30 loga+ 19" (log a) tee), 


or, putting in the numerical value of a, viz. 1:0077 (that is, 
putting log, a=°0076), | 


6=C0(266-6 + 6 + 0025 & + 000005 6 +...), 


or 


6= 06 Ps ee BSA OEY 
(267+ “Set gee) 


Remember that 0 is to be ultimately the excess of the tempe- 


208 Dr. O. J. Lodge on the Variation of the Thermal 


rature of any point of the rod over that of the enclosure. It 
may be any thing between 0° and 150°; but it is not likely in 
ordinary experiments to go above 200°. The terms of the 
above series for the extreme case 0=200 are 


267 + 200+ 100+ 40+ 1, 


where only the last term, containing the fourth power of the 
temperature, can be regarded as quite negligible. But for the 
more likely case of 6=100, the terms of the series are 


267+1004+25+5+4 ss 


where the term containing the cube of @ is not of much con- 
sequence. If, however, it were wished not to go higher than 
the second power, the term containing the cube need not be 
neglected, but a mean value of it may be added to the coeffi- 
cient of the second power of @. Thus if © be the highest 
temperature taken notice of (i. e. the temperature of the origin 
in the case of the rod, the initial temperature in the case of 
a cooling body), 
b= C0 {267 +0+0(725 + aye) bs 
<, { 400 ° 200,000/ § ’ 
and this is the expression we shall use, writing it first in the 
simpler form, 
6=C04 267+0+ Hf Bett )t (7) 
= i00( 10007 3 2 ae 
Notice that @ occurs in this expression as a factor, so that it 
is really a cubic function of 0. 

Tt is smgular how near the constant term in these brackets is to 
the number 274. I suppose this is accidental; but at first sight it 
looked as if the rate of cooling for small excesses of temperature 
were proportional to the product of absolute temperature and ex- 


ena, 
cess, or as if the quotient a would be constant. On this hypo- 


thesis, however, the constant a, twice the reciprocal of whose loga- 
rithm is the number which happens to be nearly 274, would vary 
with v, the temperature of the enclosure, which is contrary to Du- 
long’s results. Indeed there seems no ground for the conjecture. 

Applying the correction for the neglected terms of the series, as 
is done in (7), we may write the expansion (6) thus, writing @ in- 
stead of log, a for shortness (a=0076), 


eh 2s 1 aL oye i} } ry 
a?—1 2 a | 1+ 500+ 5 a°6" (1+ <00) Pe 


13. It remains now to show, from Tables of experimental 
results, to what amount of accuracy 0, multiplied by a quadratic 


Conductivity of Metals with Temperature. 209 


function of 0, will represent the observed rate of cooling of a 
body in a vacuum. 

And first I will take the experiments of Narr* (see Wiillner, 
vol. iii. p. 254). The following Table contains the result of 
his experiments in a vacuum. The first column is the observed 
rate of cooling at the Centigrade temperature shown in the 
second column, the enclosure being at zero Centigrade. The 


third column contains the product of excess of temperature ¢ 


and absolute temperature v, divided by the rate of cooling, to 
show how far this ratio is constant. These numbers are ob- 
served to decrease regularly, though slowly, and in a manner 
which has an obvious relation to the corresponding number in 
the preceding column ; so that if twenty times that number 
be subtracted from each, the result will be very constant, as is 
shown in the last column. 


a : Qin? | 2 one 
| fo | 
3.26 115 13720 11420 
311 110 13580 11380 
2-80 100 13360 11360 
2-49 90 13160 11360 
2-18 80 12990 11390 
1-88 70 12810 11410 
1°73 65 12740 11440 


Hence 
—20t= const =11400. 


We may write this, 
20t= 


or, approximately, 


: t é 
t= FiA00 (274+0)(1— su) 


which is of the form of equation (7), namely the excess of 
temperature ¢ multiplied by a quadratic factor. The nume- 
rical value of the constants do not, indeed, agree well with those 
of Dulong, especially in the fact of the sign of the coefficient 
of @ being negative; but this is hardly to be expected, as 
Narr seems to have undertaken his experiments with the object 
of upsetting Dulong’s results. Narr’s experiments, moreover, 
do not extend over any thing like the range of temperature 
that Dulong and Petit’s did. 


* Poge. Ann. vol, cxlii. 


OAT +t 
BGORE GY? e e e e e ° e (8’) 


210 On Variation of Thermal Conductivity of Metals. 


14. If we apply the same process to the Table expressing 
the results of the latter experimenters in a vacuous enclosure 
at Centigrade zero, we shall find that the number +30 has to 


be used instead of —20; so that +300 is very tolerably 


constant, and equal to 18650 on the average, as is shown in 
the following abridged Table of Dulong’s results. Consider- 
ing that the range of temperature extends as high as 240°, the 
agreement is pretty good, 


6 9. (2720) 0 neal 
) iy 
10°69 240 11530 18730 
7-40 200 12810 18800 
4-89 160 14200 19000 
3-02 | 120 15650 18050 
1-74 80 16270 18670 


Hence we may write 


306 = 


or, approximately, 


27440 
622—0° 


ae OR 8 
b= a3, (274+0)(1 ri ama) 


which is the form of equation (7). 

It may be hereafter convenient to know that an expression 
like (8) and (8”) is capable of representing the law of cooling 
in a vacuum with great accuracy, viz. £ 
an ANO 
“peag 3 «gece Sie ales ene (8) 


O,0 . gt eee 


6=C6 


but for our present purpose I think the equation (7) will be 
the most convenient. | 
15. The agreement of equation (7), as it stands, with Du- 
long and Petit’s results it is scarcely necessary to show by a 
Table, since the equation has been deduced by known approxi- 
mation from their own statement which completely expressed 
them, and the value of the terms neglected for an excess of 
temperature so high as 240° is perfectly evident. Nevertheless 
I have made the calculation, and the values of the “ constant’’ 
2 
(267 +0+ : a) * or = corresponding to the successive 
excesses of temperature 240°, 200°, 160°, 120°, and 80°, are 


I 


Notices respecting New Books. 211 
15265, 15865, 16489, 17086, and 16827. Hence the discre- 


pancy between equation (7) and experiment is not great even 

for temperatures so high as 240° ; while for a maximum tem- 

perature under 150° or so the discrepancy is practically nil. 
[To be continued. | 


XXXV. Notices respecting New Books. 


Scientific Memoirs ; being experimental Contributions to a Knowledge 
of Radiant Energy. By Joun WitttaM Drarer, W.D., LL.D., 
&c. §c. New York: Harper and Brothers. 1878 (8vo, pp. 473). 


T)R. DRAPER here brings together the scattered memoirs and 

essays that he has written during the past forty years on 
subjects connected with Radiation and Radiant Energy. They are 
thirty in number, and for the most part are simply reprints ; but 
in a few cases the original memoirs are condensed, and in one or 
two cases the article here given is the substance of a considerab!e 
number of detached articles. Most of them have already appeared 
in our pages; the earliest of them, on subjects relating to Photo- 
graphy, appearedin 1840. “I have endeavoured,” the author tells 
us, ‘‘ to reproduce these memoirs as they were originally published. 
When considerations of conciseness have obliged me to be con- 
tented with an abstract, it has always been so stated, and the place 
where the original may be found has been given. Sometimes, the 
circumstances seeming to call for it, additional matter has been in- 
troduced ; but this has always been formally indicated under the 
title of Votes, or included in parentheses” (p. x). 

It is probably known to our readers that Count Rumford made 
a donation to the American Academy of Arts and Science (similar 
to that which he made to the Royal Society) for rewarding dis- 
coyeries and improvements relating to light and heat made in 
America. The Academy has been rather chary of bestowing its 
honours, and had only awarded its Rumford Medal four times before 
it made the award in 1875 to Dr. J. W. Draper “ for his researches 
in Radiant Energy.” This circumstance has determined the se- 
lection of articles in the present volume. It comprises the re- 
searches on which the Award was founded. 

The President’s statement of the grounds of the Award is given 
in the Appendix, and may be summarized as follows :— 

(a) Independent discovery of Moser’s Images. ; 

(5) Measurement of the Intensity of the Chemical Action of 
Light by exposing to the Source of light a mixture of Equal Vo- 
lumes of Chlorine and Oxygen. 

(c) Application of Daguerreotype process to taking portraits. 

(d) Application of ruled glasses and specula to produce Spectra 
for the study of the Chemical Action of light. 

(¢) Investigation of the nature of the rays absorbed by growing 
plants in sunlight. 


212 Notices respecting New Books. 


(f) Discussion of the Chemical Action of light and proof that 
rays of all wave-lengths are capable of producing chemical changes. 

(g) Researches on the distribution of Heat in the Spectrum. 

And, finally,an elaborate investigation, publishedin 1847, by which 
he established experimentally the following facts, which we will 
give in the words of the Award :— 

“1. All solid substances, and probably liquids, become incan- 
descent at the same temperature. 

“2. The thermometric point at which substances become red- 
hot is about 977° Fahr. 

“3. The spectrum of an incandescent solid is continuous ; it con- 
tains neither bright nor dark fixed lines. 

“4, From common temperatures nearly up to 977° Fahr. the 
rays emitted by a solid are invisible. At that temperature they 
are red; and the heat of the incandescmg body beg made con- 
tinuously to increase, other rays are added increasing in refrangi- 
bility as the temperature rises. 

“5, While the addition of rays, so much the more refrangible as 
the temperature is higher, is taking place, there is an increase in 
the intensity of those already existing.” ‘The Award then proceeds 
as follows :— “ Thirteen years afterwards Kirchhoff published his 
celebrated memoir on the relations between the coefficients of 
emission and absorption of bodies for light and heat, in which he 
established mathematically the same facts and announced them as 
new.” 

We are, of course, aware that this is rather a burning question ; 
but whatever may be thought of the justice of these claims, there 
can be no doubt that the fact of their having been made on behalf 
of Dr. Draper by so distinguished a body as the American Academy 
of Arts and Science ought to be known, and that its judgment 
will receive at least respectful consideration whenever the early 
history of Spectroscopic Science comes to be written. And it is 
impossible not to draw attention to the fact in a notice, however 
brief, of Dr. Draper’s volume; for plainly one of the motives of its 
publication is to assert his claims to priority of discovery in re- 
gard to the points above quoted. In fact the four memoirs which 
bear directly on the subject of Spectrum Analysis are printed first 
in the volume, and are followed by a note in which Dr. Draper 
complains, though in very decorous language, that he has received 
considerably less than justice at the hands of M. Kirchhoff ; and by 
way of showing that he has tangible grounds for complaint, he makes 
the following quotation (p. 85) from M. Jamin’s Cowrs de Physique, 
in which results that he had previously established are formally at- 
tributed to M. Kirchhoff. | 

“M. Kirchhoff has deduced the following important conse- 
quences :— 

“Black bodies began to-emit at 977° Fahr. red radiations, to 
which are added successively and continuously other rays of in- 
creasing refrangibility as the temperature rises. 


Notices respecting New Books. 218: 


_ * All substances begin to be red-hot at the same temperature in 
the same enclosure. 

“ The Spectrum of solids and liquids contains no fixed lines.”* 

- Now it may be said with very little qualification that what is here 
attributed to M. Kirchhoff is to be found distinctly stated in the first 
memoir in the volume before us, which was published by Dr. Draper 
in 1847. By experimenting with a strip of platinum heated by the 
transmission of a current whose force could be regulated, he ascer- 
tained that the temperature at which red rays are first radiated is 
977° Fahr. He also ascertained that platinum, brass, antimony, 
gas-carbon, and lead became incandescent at the same time with 
the iron barrel in which they were gradually heated, and that the 
apparent exceptions presented by chalk, marble, and fluor-spar 
were due to phosphorescence. By raising the temperature of the 
platinum wire and analyzing with a prism the light emitted, he 
proved that the length of its spectrum gradually increased with the 
temperature until at 2130° Fahr. the full spectrum of daylight 
was attained ; and-it is clear that he regarded the result thus ob- 
tained as being generally true. That the spectrum of the incan- 
descent platinum contained no dark lines did indeed come out only: 
incidentally in the course of the investigation: still it was not by 
any means a point seen but not observed; for, in consequence of 
observing it he resorted to a comparison of the spectra of incan- 
descent platinum at different temperatures with the spectrum of 
daylight in order to determine their extent, instead of fixing their 
extent by the dark lines of the spectra themselves, which he had as- 
certained to be non-existent. On the whole the above statement 
breaks down at nearly every point. What is therein referred to 
M. Kirchhoff was certainly ascertained before by Dr. Draper. 
Whether Dr. Draper was the first person to observe all these points 
is a very different question, and one we would by no means pre- 
judge ; indeed, without going beyond the limits of the first memoir, 
it is pretty plain that the temperature of incandescence was known 
with considerable accuracy before Dr. Draper’s experiment with 
the platinum wire ; and it certainly was believed (if not proved) 
that the temperature was the same for all bodies. 


Geological Survey of Canada. Report of Progress for 1876-77. 
week. ©. Senwyn,, 7S. £.G.S3 Director... 8v0: Pp. 531. 
Dawson Brothers: Montreal, 1878, 


Besides the Introductory Report by the Director, this volume 
contains the following important Reports:—1. On Geological Ex- 
ploration in British Columbia, chiefly on the Blackwater, Salmon, 
and Nechaco Rivers and Francois Lake; by G. M. Dawson; with 
coloured map and seven very suggestive plates of local scenery. 

* The above quotation is, we presume, to be found on pp. 463, 464, vol. iii. ed. 
1866. If so, it is not exactly a quotation, but is made up of parts of a much 
longer statement. We may also observe that Memoir I. of the present volume 


is not in all respects an exact verbal reprint of the Memoir published in our 
Journai for May 1847. This does not, however, affect the point at issue. 


Phil. Mag. 8. 5. Vol. 7. No. 42. March 1879. R 


214. Notices respecting New Books. 


2, Reconnaissance of Leech River and Vicinity (auriferous) ; by G. 
M. Dawson. 3. The Mines and Minerals of British Columbia 
(Gold, Coal, Lignite, Iron, Silver, Copper, &c.); by G. M. Dawson. 
4. Jurassic fossils from the Iltasyouca River, British Columbia ; 
by J. F. Whiteaves. 5. Coal-fields of Vancouver and neighbouring 
islands, and the Tertiary rocks of Sooke Bay, &c.; by James 
Richardson ; with coloured map and sections. 6. Geological Re- 
search north of Lake Huron and east of Lake Superior ; by Robert 
Bell. 7, The Goderich Salt Region ; by T. Sterry Hunt. 8. Geo- 
logy of the Counties Renfrew, Pontiac, and Ottawa, with their 
iron-ores, apatite, and plumbago ; by H. G. Vennor; with coloured 
map. 9. The Slate-formations and general Geology of Charlotte 
Co., New Brunswick; by G. F. Matthew. 10. Lower Carboni- 
ferous belt, including the Albertite and its shales &c., in New 
Brunswick; by L. W. Bailey and R. W. Ellis; with map and ~ 
sections. 11. Geology of part of Cape Breton, with notices of the 
coals and metals (including gold) found in the vicinity ; by Hugh © 
Fletcher ; with coloured map. 12. Additions to the Insect fauna 
of the Tertiary beds at Guesnel, British Columbia; by Samuel 
Scudder. 13 and 14. Notes on Rocks and Minerals; by B. J. 
Harrington and Christian Hoffmann. 

_ A comprehensive Index completes this volume, which is full of 
important information, interesting in every branch of geological 
research—physiographic, stratigraphic, paleontographic, petrogra- 
phic, and mineralogical,—so much so, indeed, that the mere list of 
main subjects alluded to above, must indicate to any one that 
veteran geologists will see many of the old classic regions of North- 
American geology greatly elucidated by modern research, and 
rising students will have to congratulate themselves on difficulties 
having been removed from their paths, and a very wide and clear 
field opened in many directions for their own researches. To the 
political and social economist the explanation and mapping of the 
soils, structure, and mineral products of the great Canadian Domi- 
nion is necessarily of immeasurable importance; and the good 
useful work brought to general comprehension in this Report is 
therefore an Imperial benefit. 


Remarks on the Sedimentary Formations of New South Wales. 
Illustrated by References to other Provinces of Australia. By the 
Rev. W. B. Crarxzn, M.A., F.RS., F.GS., ge. Fe. Fourth 
Edition. S8vo. Pp. 165. Richards, Sydney; Tribner, London, 
1878. 


Well worthy of being recorded among the early race of Geologists, 
who worked out their views of the science as presented by the 
phenomena observed, and defined by the general knowledge with 
which they had enriched their natural genius, the late W. B. 
Clarke was one of those who were led by special taste to cultivate 
the natural-history sciences before schools and colleges provided 
means of definite instruction in these matters. His first geological 
observations were published in an early series of the Magazine of 


Geological Society. 215 


Natural History. After his settling in Australia he followed his 
bent in Geology, and got an insight into the general structure of 
the eastern mountain-ranges and of the strata flanking them on the 
east; and he was one of the first to recognize the gold-drifts and 
auriferous rocks. The relative position and age of the Coal- 
measures there he also studied; and he philosophically concluded 
that certain plant-remains in the Australian coal did not neces- 
sarily give it a Jurassic age, or remove it from the Paleozoic series, 
because they resembled, or even were identical with, a fossil plant 
found in the Oolites of Yorkshire. The persistence of many low 
organisms, the wide extent and long-continued emigration of suc- 
cessions of similar creatures, as well as other considerations, strongly 
supported the veteran observer in his discussions with those who 
would draw equally definite demarcations for the extinct fauns and 
floree of Britain and for those of its antipodes. Of this and many 
other subjects, interesting to both the historian and the student of 
geology, this last edition of Mr. Clarke’s condensed observations 
covtains a complete account, involving, too, a considerable series of 
notes on the geological structure and history of other regions. It 
was finished on June 2, 1878, the eightieth birthday of the enthu- 
siastic author, who had for many years given his best exertions to 
the elucidation of Australian geology, to its beneficial application 
to his fellow countrymen, and to the dissemination of a sound 
knowledge of his favourite science to all whom his words and 
writings could reach. He ceased from his labours before the year 
was out, respected and honoured, leaving behind him the legacy of 
good work, with its sure results in advancing the welfare of his 
fellow men. 


XXXVI. Proceedings of Learned Societies. 


GEOLOGICAL SOCIETY. 
[Continued from p. 143. ] 


Jan. 22, 1879.—Henry Clifton Sorby, Esq., F.R.S., President, in 
the Chair. 


| fe following communications were read :— 
ui 


. “On Community of Structure in Rocks of Dissimilar Origin.” 
By Frank Rutley, Esq., F.G.S. 

After alluding to the community in mineral constitution of certain 
rocks to which different names have been applied, and indicating 
the advisability of retaining some old terms in a provisional 
sense, questions relating to the causes of the angular and rounded 
characters of certain rock-constituents were discussed. The 
author then described some of the more common structural 
peculiarities met with in rocks of various origin, especial at- — 
tention being directed to those in which microcrystalline, eryp- 
tocrystalline, or microfelsitic conditions have been either nor- 
mally developed or superinduced; while other rocks were de- 


216 Intelligence and Miscellaneous Articles, 


scribed in which corresponding structure, sometimes coupled with 
a similar mineral constitution, may be met with. Difficulties 
attending the determination of the origin of some clastic rocks were 
also pointed out, and the value of certain structural characters in 
their diagnosis were mentioned. Assumptions as to the origin of 
some fragmentary rocks were shown to be undemonstrable in certain 
cases, although such assumptions often carried much probability 
with them. The resemblances presented by devitrified rhyolitic 
rocks, felstones, and felspathic grits were dwelt upon at some length. 
The paper included a short structural classification of the con- 
stituents of rocks. 


2. “Distribution of the Serpentine and associated Rocks, with 
their Metallic Ores, in Newfoundland.” By Alexander Murray, lsq., 
C.M.G., F.G.8. 

The author stated that no eben dierileae of serpentine is 
known in the Laurentian series in Newfoundland ; nor is the existence 
of crystalline limestone of that age, with aiee serpentine is often 
associated, as yet well established. The Intermediate or Huronian 
system is singularly barren in lime, magnesian minerals, and mica, 
lime occurring almost exclusively as intersecting calcareous veins. 
Over all the known area of the system no masses of serpentine have 
been observed, and only one instance of the presence of a serpen- 
tinous mineral, which occurs in an intrusive mass intersecting the 
Intermediate system and disturbing the outcrop of the sandstones 
of the Primordial Silurian (Lingula Flags) at a place called “The 
Broad” of Tickel Harbour, Trinity Bay, where some steatite with 
some seams of asbestos were seen near the contact. Wherever a 
typical fossiliferous horizon could be established, the stratigraphical 
position of the fossils placed those of the Lévis age, or older, below 
the serpentines ; while in all cases, where the types were of Hudson- 
River or newer date, they as invariably succeeded unconformably 
above. Instances of this unconformable relation were mentioned in 
which the upper formation was as late as the Devonian age. The 
stratigraphical and paleontological break between the Levis and 
Trenton groups is here filled up by a metamorphic mass which, in 
part at least, may possibly represent the horizon of the Chazy group ; 
and the great intrusive masses have been connected with, or the 
cause of, the metamorphic phenomena displayed. 


XXXVII. Intelligence and Miscellaneous Articles. 


ON THE ELECTROMAGNETIC THEORY OF THE REFLECTION AND 
REFRACTION OF LIGHT. BY GEORGE FRANCIS FITZGERALD, 
M.A., FELLOW OF TRINITY COLLEGE, DUBLIN. 

(( ES media, at whose surfaces reflection and refraction are sup- 


posed to take place, are assumed to be nonconductors, andisotropic 
as regards magnetic inductive capacity. Some reasons are adyanced 


| 


ee Oe 


Intelligence and Miscellaneous Articles. 217 


why the results should apply at least approximately to conductors. 
In the first part of the paper the media are not assumed to be iso- 
tropic as regards electrostatic inductive capacity ; so that the results 
are generally applicable to reflection and refraction at the surfaces 
of crystals. I use the expression given by Professor J. Clerk Max- 
well in his ‘ Electricity and Magnetism,’ vol. i. part 4, chap. 11, for 
the electrostatic and electrokinetic energy of such media. By assu- 
ming three quantities £, 7, and Z, such that, ¢ representing time, 
ae and 3 are the components of the magnetic force at any 
a G 

point, I have thrown these expressions for the electrostatic and 
electrokinetic energy of a medium into the same forms as M‘Cullagh 
assumed to represent the potential and kinetic energy of the ether, 
in “ An Essay towards a Dynamical Theory of Crystalline Reflection 
and Refraction,” published in vol. xxi. of the Transactions of the 
Royal Irish Academy. Following a slightly different line from his, 
I obtain by a quaternion and accompanying Cartesian analysis, the 
same results as to wave-propagation, reflection, and refraction as 
those obtained by M‘Cullagh, and which he developed into the 
beautiful theorem of the polar plane. Of course, the resulting 
laws of wave-propagation agree with those obtained by Professor 
Maxwell from the same equations by a somewhat different method. 
For isotropic media, the ordinary laws of reflection and refraction 
are obtained, and the well-known expressions for the amplitudes of 
the reflected and refracted rays. 

In the second part of the paper I consider the case of reflection 
at the surface of a magnetized medium, adopting the expressions 
Professor J. Clerk Maxwell has assumed in ‘ Electricity and Mag- 
netism, vol. u. part 4, § 824, to express the kinetic energy of such 
amedium. From this, following the same line as before, i have 
deduced the following equations to represent the superficial condi- 
tions. In them &, n, ¢ have the same meaning as before, and the 
axes are w in the intersections of the plane of incidence and the 
surface, y in the surface, and z normal to it; a, 6, y are the com- 
ponents of the strength of the vortex that Professor Maxwell 


assumes, and 


ad ad d d 
ah es Vie ee 


which, with these axes, reduces to 


ad d 
paab tape: 


K and K, are the electrostatic inductive capacities of the two media 
in contact ; and the quantities referring to one of these which is 
supposed to be non-magnetic are distinguished by the suffix ,; C is 
a constant, on which the power of the medium to rotate the plane 
of polarization of light depends. 


218 Intelligence and Miscellaneous Articles. 


ab onde) 1 Ade dL\. © An OK, { dn dn } 


da, K\dz de "dedi ' dhdt 


dn, __K, dn {7 d(dé_ dé aE 
Pee ee tae ge) a 

As these are unchanged by a simultaneous alteration of the signs 
of 7 and C, I show that the method adopted in my former paper on 
Magnetic Reflection, in the ‘ Proceedings of the Royal Society’ for 
1876, No. 176, is justified, and that it is legitimate to consider an 
incident plane-polarized ray as composed of two oppositely circu- 
larly polarized rays, each of which is reflected according to its own 
laws. From these I further deduce that, when the magnetization 
of the medium is all in the direction of n, there is no effect on reflec- 
tion or refraction produced by it. I consider next the cases of the 
magnetization being all normal to the surface, and all in the surface 
and the plane of incidence, and obtain the following result :— When 
the incident ray is plane polarized, and the plane of polarization is 
either in or perpendicular to the plane of incidence, the effect of 
magnetization is to introduce a component into the reflected ray 
perpendicular to the original plane of polarization, whose ampli- 
tude, ¢, is given in the several cases by the following equations, in 
which 2 is the angle of incidence, and r of reflection, and & a small 
constant depending principally on C and the intensity of the mci- 
dent ray 1. When the magnetization is normal to the reflecting 
surface. If the incident ray be polarized in the plane of incidence, 

tale (1+ cos’r) sin® 7 sin 22! 
~ “sin. sin? (Z@+7r) .cos (i—r) 
If it be polarized in a plane perpendicular to the plane of incidence, 
cos’r .sin®2 sin 22 
sin7.sin?(¢+7r).cos (¢@—7) 

2. When the magnetization is parallel to the intersection of the 
surface and the plane of incidence, and the plane of polarization of 
the incident ray is either in or perpendicular to the plane of inci- 
dence, 


dz 


i 


35. COS sin? ¢ sin 27 
sin? (¢+7r) cos (t—r) 

This vanishes at the grazing and normal incidences, and, in the case 
of iron, attains a maximum at about the angle of incidence i= 63° 20!. 

I do not obtain any change of phase by reflection in any case; 
and this was to be expected, as this change of phase probably depends 
on the nature of the change from one medium to another, which, 
following M‘Cullagh, I have uniformly assumed to be abrupt. 
Apart from this question of change of phase, my results conform 
completely to Mr. Kerr’s beautiful experiments on the reflection 
of light from the pole of a magnet, as published in the Philoso- 
phical Magazine for May 1877 and March 1878.—Proceedings of 
the Royal Society, January 9, 1879. 


Intelligence and Miscellaneous Articles. 219 


ON THE VELOCITY OF VERY LOUD SOUNDS. BY WILLIAM W. 
JACQUES, FELLOW OF THE JOHNS HOPKINS UNIVERSITY. 


It is very well known that the velocity of a musical sound is, 
within very wide limits, sensibly independent of its imtensity 
and of its pitch. The experimental proof of this is that a piece 
of music, played by a military band at a considerable distance, 
comes to the ear of the observer with its harmony entirely un- 
disturbed. 

A consideration of the theory of the propagation of a musical 
sound, too, shows that for sounds such as we ordinarily hear, in 
which the change of density from the rarefied to the condensed 
portion of the wave is small compared with the density of the 
undisturbed air, the velocity should be independent both of the 
intensity and the pitch. 

When, however, we come to the consideration of a loud and 
sharp shock or explosion, in which the disturbances are very vio- 
lent and abrupt, we cannot be at all sure that the changes of 
density are negligibly small, and hence that the velocity of sound 
for such cases. would be a constant. 

So little is known of the conditions in the case of the formation 
and propagation of sound from a centre of explosion, and the 
mathematical considerations of such conditions as we may presume 
are so difficult, that we must look almost entirely to experiment 
for our knowledge of the propagation of very loud sounds. But 
our experimental evidence on this point is very limited. Nearly 
all of the experiments that have been made upon the velocity of 
scund have been made with cannon, and have not agreed re- 
markably well with each other; nor have the thermodynamic quan- 
tities calculated from them, on the supposition that the velocity 
is identical with that of a musical sound, agreed very well with 
the values of the same quantities determined by other methods. 
But we cannot say whether these errors are due to the character 
of the sound or to other causes. 

The very short interval between the flash and the report of a 
stroke of lightning, even when it takes place at a considerable 
distance, has been instanced* as a proof of the greater velocity of 
very loud sounds; but, so far as the writer is aware, this has not 
yet been reduced to experiment. 

The experiments of Regnault ? in water-pipes showed that the 
velocity of a pistol-report became slightly less each time that it 
was reflected along the pipe; but the change was very small, and 
its cause is doubtful. ! 

The following paper contains an account of some automatic 
measurements of the velocity of sound in the immediate vicinity 
of acannon. ‘The results show that the velocity near a cannon is 
considerably different from that at a distance, and point out a 


* Earnshaw, Phil. Mag. 1860. i Regnault’s * Memoirs,’ 


220. Intelligence and Miscellaneous Aptis, 


considerable error that has been introduced into the most impor- 
tant measurement of this quantity. : 

The experiments were made at the United-States Arsenal in 
Watertown, Mass. 

- The method used was an automatic measurement of the velocity 
at different distances (varying from 10 to 110 feet) from the mouth 
of the cannon, by means of a series of membranes* electrically 
connected with a chronograph. | 

In the midst of a large level field was placed a six-pound brass 
field-piece. In the rear of this, at distances of 10, 30, 50, 70, 90, 
and 110 feet from the mouth of the cannon, were placed the mem- 
branes, elevated about 3 feet above the ground. These membranes 
consisted each of a hoop 9 inches in diameter, over which was 
stretched a sheet of thin rubber. ‘To the centre of the membrane, 
and on the side towards the cannon, was attached a very small 
shelf of polished brass. Upon this rested one end of a delicate 
steel spring, the other end being fixed to an independent support. 

The wire ‘that brought the current of electricity from the chro- 
nograph-house was connected with the spring; and from the shelf 
a second wire returned to the chronograph. When the spring 
rested upon the shelf the circuit was closed; the passage of the — 
sound-wave, however, would move the fete one. and break the 
circuit, causing a register on the chronograph. When the spring 
fell it rested upon a contact-point, from which a wire ran to the 
next membrane of the series ; so that the circuit, immediately after 
being broken at the first membrane, was made again through the 
second before the sound-wave reached it. In this way the current 
could be transferred to all the membranes of the series, and the 
successive breakings and makings of contact, as the sound-wave 
passed each one, could be registered on a chronograph placed at a 
distance. 

The chronograph used was of the Schultz form, and consisted 
essentially of a rapidly and uniformly revolving cylinder of silver, 
covered with lampblack, which was made one pole of the secondary 
coil of an inductorium, the primary coil of which was in circuit 
with the membranes. ‘The other pole of the secondary coil was a 
fine metal point brought very near to the surface of the cylinder. 
When the primary circuit was broken or completed at the mem- 
branes, a spark passed between the metal poit and the cylinder, 
and made a fine dot in the lampblack. By the side of the point 
was an electrical tuning-fork, which traced a sinuous curve of times 
on the lampblacked surface of the cylinder. The time could thus 
be measured to ‘00001 of a second. All that was necessary then 
for the experiment was to choose a moment when the air was as 
nearly as possible at rest, and then, the membranes being in order, 
to start the chronograph and fire the gun. The distances between 
the membranes were then accurately measured, the times of passage 
between successive membranes determined from the chronograph, 


* Regnault used membranes, though unlike these, in his water-pipe 
experiments. 


Intelligence and Miscellaneous Articles. 221 


and the temperatures read off from thermometers placed at each 
membrane. 

The experiment was many times repeated with the membranes 
interchanged, with different velocities and parts of the chronograph- 
cylinder, and with other precautions, to prevent possible errors, 
but always with the same result. It was found that immediately 
in the rear of the cannon the velocity of sound was less than at a 
distance, but that going further and further from the cannon the 
velocity of sownd rose to a maximum considerably above the ordinary 
velocity, and then fell gradually to about the velocity usually recewed. 

Tn order to determine whether the first low velocities were due, 
as was supposed, to the retarding influence of the bodily motion of 
the air around the cannon, it was pointed at right angles to its 
first position, when it was found that the maximum velocity came 
nearer to the cannon. Had the cannon been turned in the direc- 
tion of the line of membranes, the retardation would probably have 
become an acceleration. The experiment was, however, of course 
impracticable. That this apparent retardation was not due to the 
difference in time of action of the membranes (due to a variation 
of the force of the wave) is evident both from the very slight force 
required in either case, and from the fact that the variation noticed 
is in the wrong direction. 

The charge of powder was considerably varied ; and the heaviest 
charges, of course, caused the greatest deviation from the ordinary 
velocity. 

The successive series of experiments, owing to differences in the 
charge and in the loading, gave different values of the velocity at 
any one place; but the facts above stated always remained. the 
same. 

Accordingly each series represents the condition of things better 
than the mean of several, and I have here given a table of three 
of the best series. 

The first column represents the distance from the mouth of the 
cannon, the second the values of the corresponding velocities in 
the rear of the cannon when the charge was one and a half pounds, 
the third when the charge was reduced to half a pound, and the 
last when the cannon was pointed at right angles to the line of 
membranes. 

Velocities reduced to 0° C. 


Rear of cannon. Side of cannon. 
Interval. 13 lb. 2 lb. 
10-— 30 feet. 1076 feet. 
30=.50..,, PAK e) iss 0h is 1032 1067 
50-70, % 1240 ,, 1091 1162 
70—- 90 ,, 12GB T ics. 1120 1201 
90-110 ,, 1262 _,, 1114 1188 


The conclusions that we may draw from these experiments 
are:——1. That the velocity of sound is a function of its intensity. 
2. That experiments upon the velocity of sound in which a cannon 
is used contain an error, probably due to the bodily motion of the 


Phil. Mag. 8.5. Vol. 7. No. 42. March 1879, S 


222 Intelligence and Miscellaneous Articles. 


air near the cannon. Evidently a musical sound of low intensity 
must be used for a correct determination of the velocity of sound. 
—Silliman’s American Journal, February 1879. 


—_— 


RESEARCHES ON BELL’S TELEPHONE. BY HENRI DUFOUR. 


The principles on which the construction of Bell’s telephone is 
based are direct consequences of the phenomena of imduction and 
electromagnetism; and from theoretical considerations all that 
passes in that instrument can be foreseen. When it is employed 
we are struck, on the one hand, with the minuteness of the vibra- 
tory motions necessary to produce magnetic modifications of the 
magnet and the induction resulting from it, and, on the other, with 
the relatively great intensity of the sounds produced. 

It seemed to me that it would be interesting to verify upon a few 
instruments the principal phenomena which theory enables us to 
foresee, and to seek out some of the causes which may modify 
them. 

The instruments employed were constructed by M. J. Cauderay, 
at Lausanne. The mean length of the magnet was 127 millims., 
the thickness of the vibrating plate from 0°159 to 0-175 millim. 
The induction-coil contained 46 metres of wire of 0:3 millim. 
thickness. 

Intensity of the Currents —The maximum intensity observable is 
obtained by pressing on the vibrating plate so as to bring it mto ~ 
contact with the soft-iron termination of the magnet; the dis- 
placement it thus undergoes is about 1 millim., and produced a 
deflection of 7—8° upon the galvanometer which I ‘used. An equal 
deflection in the opposite direction is observed when the plate re- 
sumes its initial position. 

The movement of the plate towards the magnet renaea an in- 
verse induced current in the three instruments which I tried, the 
pole of the magnet being in fact behind the coil through which 
passed the cylinder of soft iron. 

For the purpose of knowing if the two currents, direct and in- 
verse, possess an appreciable difference of intensity, the wires of 
the telephone were put into communication with two carbon elec- 
trodes dipping in water, and which could be connected with the 
galvanometer by means of a commutator. <A great number of 
vibrations of the plate were produced, so that a series of induced 
currents, direct and inverse, traversed the liquid; the electrodes 
connected with the galvanometer gave no polarization-current. 
From this we may conclude that the difference of intensity of the 
two currents is very slight. In the construction of the telephone, 
therefore, no account is to be taken of the action which this 
difference may in time exert upon the magnetization of the bar. 

Two of the instruments employed had~ poles of opposite names 
submitted to the action of the coil; and when joined they worked 
as well as those which are symmetric. 

_ Intensity of the Maynetism.—The variations of intensity of the 

agnetism were ascertained in the following manner :—The north 


Inielligence and Miscellaneous Articles. 223 


pole of the magnet of a Weber's magnetometer was submitted to 
the simultaneous action of the south pole (surrounded by the coil) 
of a telephone A and the south pole of a magnet; these two 
instruments were placed so that the bar of the magnetometer was 
in equilibrium between them. A second telephone, B, was in 
communication with A. The movements of the mirror of the 
magnetometer were observed by the ordinary method of reflection 
of the divisions of a rule in the field of a telescope. 

A pressure exerted upon the plate of B permitted a slight dis- 
placement of the magnet to be ascertained ; but the movement was 
too small to be measured; its direction was always that which the 
theory caused to be foreseen. 

Vibrations of the Plate—Some attempts were made to determine 
the vibrations of the plate. The first method employed consisted 
in transmitting the vibrations toa gas-flame. For this purpose 
the wide-mouthed bell of the telephone was replaced by a cylindrical 
one of small capacity. A cork, pierced with two holes through 
which passed two kneed tubes of glass, bounded within the cylinder 
a sort of little chamber comprised between the front face of the 
vibrating plate and the hind face of the cork. The illuminating- 
gas entered through the first tube, and issued, forming a small 
flame, at the extremity of the tapering second tube; so that the 


_ whole constituted something analogous to the manometric capsules 


which M. Konig places upon the pipes. 

Every vibration of the plate is betrayed by a movement of the 
flame when the induced currents employed are those produced by 
a small Dubois-Reymond coil, even when the exterior coil is at 2 
centims. from the extremity of the inducing coil. The currents 
produced by the voice in a second telephone cause no variation in 
the height of the flame. 

_ The result was equally negative when a small mirror was borne 
on a kneed lever with its end resting on the vibrating plate. A 
ray of light reflected by the mirror did not appear to be displaced 
under the influence of the vibrations produced by the voice. 

Finally, I tried to produce coloured rings between the vibrating 
plate and a lens placed upon it. For this a very thin piece of glass 
(Deckglaschen) was placed upon the vibrating plate, in contact 
with the slightly convex lower face of alens. The sounds were 
transmitted by the instrument, although weakened. The coloured 
rings were observed through a telescope furnished with a reticule. 

The displacement of a bright ring to the following dark one is 
produced by a difference in the thickness of the stratum of air 
equal to a quarter of a wave-length ; that is to say, a change in the 
position of a yellow ring will be ascertained for about 0-000143 
millim. displacement of the plate. This displacement is mani- 
fested by a diminution in the distinctness of the rings, which 
oscillate about their normal position. The displacements are 
observed very distinctly by employing the induced currents of a 


-Dubois-Reymond coil ; but it has not been possible to verity them 


for the currents produced by the voice. 
Having heard it said that two telephones the localities of which 


224 Intelligence and Miscellaneous Articles. 


have very different temperatures do not work well, I desired to 
put the matter to the test by direct experiment. One of the in- 
struments was left during several hours exposed to a temperature 
of —18°, while the other passed the same time in an enclosure 
heated to 40° ©. The two instruments, put in communication, 
transmitted speech perfectly. 

As soon as the telephone was employed on the telegraph-lines, 
the action was remarked which is exerted upon the instrument by 
the currents used to work the Morse apparatus, and passing in — 
wires near that which connects the two telephones. This action 
is attributable to an induction-phenomenon, to a deflection, or 
perhaps to both causes combined. I have tried directly at what 
distance an intermittent current can produce an induced current 
appreciable with the telephone. 

Two copper wires, perfectly insulated, were stretched parallel 
over a leneth of 15:2 metres, and at distances varying between 15, 
35, and 45 centimetres. One of the wires joined the pile and the 
manipulator with the receiver of a Morse apparatus; the earth-line 
was formed by the gas-pipes. The two extremities of the other 
wire communicated directly with the telephone. The current 
employed produced a deflection of 60° on a telegraph-compass. 
Under these conditions all the motions of the manipulator were 
distinctly perceived ; and I am persuaded that a telegraphist would 
have understood the signs produced by the manipulator, even when. 
the distance between the two wires was 45 centimetres. 

It may hence be concluded, therefore, that on telegraph-lines 
the noise heard in the telephone when a message traverses a neigh- 
bouring wire may be attributed, at least in part, to induced currents. 
This experiment may have a certain interest in the lecture-room, 
to show at what distance an induced current can be produced. In 
this respect the telephone is much more sensitive than the galva- 
nometer.— Bibliotheque Universelle, Archives des Sciences Physiques 
et Naturelles, No. 1, 1879, pp. 91-95. 


HARMONIC ORBITS. 
To the Editors of the Philosophical Magazine and Journal, 


GENTLEMEN, 
M. Th. von Oppolzer’s “ Vulcan ”-orbit (Comptes Rendus, Jan. 6, 
1879) represents another of my predicted harmonic orbits :— 


Distance. Time. 
Von Oppolzer........ 123 58°8 days. 
Chase, prediction .... ‘120 HB ae ry. 


This leaves only one “missing link” in my triple series of prin- 


cipal harmonics, extending from a Centauri tothe Sun. There are 

many secondary harmonics, indicating possible asteroidal positions. 

One of these has been confirmed by Mouchez’s second Watson orbit. 
Faithfully yours, 


Haverford College. Pennsylvania Pumny EB. CHASE. 
February 10, 1879. 


T HE 
LONDON, EDINBURGH, axp DUBLIN 
PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES.] 


ie tut J, 1319. 


XXXVIII. The Existence of the Luminiferous Ether. By 
Ervest H. Coox, B.Sc., A.R.C.S., Lecturer on Physics at 
the Bristol Trade and Mining School*. 


4 deat enormous velocity with which the motion producing 

light is propagated through space induced the authors of 
the undulatory theory to seek about for some medium capable 
of transmitting the vibratory movement. Applying the known 
laws of the propagation of sound, which is also a vibratory 
movement, this medium must possess enormously high elas- 
ticity and extremely small density. Such a medium is the 
luminiferous ether. This substance fills all space, and is im- 
prisoned between the atoms of all bodies. The vibrations of 
the atoms of luminous bodies are communicated to the ether, 
and by it transmitted in all directions. Hach particle of the 
ether makes a small movement to and fro; but the whole mass 
is thrown into wave-like motions. The elasticity or density 
of the ether in free space is different from that of the same 
ether when imprisoned by the molecules of material bodies. 
Thus in a refracting body like glass, the elasticity of the ether 
is less (or its density is greater) than in air, and the elasticity 
in air is less than in a vacuum. We therefore find that the 
velocity of light in glass is less than it is in air, and is less in 
air than it isin avacuum. Moreover in most crystalline sub- 
stances the elasticity of the ether is different in different 
planes ; and we find that light traverses such substances with 
different velocities in different directions. The explanation 

* Communicated by the Author. 
Phil. Mag. 8. 5. Vol. 7. No. 48. April 1879. IE 


226 Mr. HE. H. Cook on the Existence of — 


given of this is that the different grouping of the molecules 
along certain lines in the crystal determines a different ar- 
rangement of the ether particles along these lines also. The 
existence of this ether was, and is, considered of such impor- 
tance by the supporters of the undulatory theory, that we find 
attempts being made to determine experimentally some of its 
properties. Thus Fizeau has arrived at the conclusion that 
a moving body drags part of the ether along with it in its 
motion. Stokes accounts for aberration by attributing to the 
ether the properties of an elastic solid. In fact, all our phi- . 
losophers accept without reservation the material existence of 
the luminiferous ether. It is impossible to fail to note the 
analogy between some of the propositions of this theory and 
those of the two-fluid theories of Magnetism and Electricity. 
These fluids also are imponderable, invisible, yet all-pervading. 
They interpose themselves between the molecules of bodies, 
and are rendered evident to us only by the effects they pro- 
duce when treated in certain ways. If we accept all these 
theories, we must assume that between the molecules of every 
unfortunate body we have five distinct fluids—two magnetic, 
two electric, and the ether. Why do we not discard the four 
and retain the ether ? and attribute to it some other proper- 
ties which would enable it to perform the functions of the 
magnetic and electric fluids? We should then only have to 
imagine the existence of one hypothetical medium. But as 
an effort of the imagination, the invention of five hypothetical 
fluids is as easy.as the invention of one. 

In order, then, to obtain for light the enormous velocity 
which experiment has shown it to possess, the supporters of 
the undulatory theory have boldly filled all space with a sub- 


stance which, conforming to the equation v=a/ <, possesses 


very great elasticity and very little density. The velocity 
with which light travels through air we may take to be 185,000 
miles per second. Sound, let us suppose, travels at 1100 feet 
per second. light therefore travels 888,000 times as fast 
through air as sound does. To find what proportion exists 
between the density and elasticity of the air and ether, let us 
suppose the velocity of sound through air to be equal to 1000 
feet per second (in this calculation the correct velocity is, of 
course, 916 feet per second). Then we have 


elast. of air : elast. of ether :: 1000? : (185,000 x 5280)”, 


assuming the density to remain constant. This gives us 
954,138,240,000 as the number of times that the elasticity of 
the ether is greater than that of the air, assuming the density 


the Luminiferous Ether. 227 


to remain constant. If we assume the elasticity to remain 
constant, we have that the density of the ether must be this 
number of times less than the density of the air. The neces- 
sity for the existence of the ether therefore is, that we 
require a body whose elasticity shall be this number of times 
greater, or whose density shall be this number of times less, than 
that of the air. It is hardly necessary to add that we know 
of no such body in nature; and since we cannot conceive of 
motion without having something moved, we invent the hypo- 
thetical substance ether, which shall be the vehicle of our wave- 
motion. But have we not been too eager to invent ? have we 
thoroughly satisfied ourselves that matter itself (¢. e. ordinary 
matter) is incapable of transmitting the vibratory movement ? 
In attempting to answer these questions, we have first to show 
that the theory of the constitution of the luminiferous ether as 
at present held is untenable; and, secondly, we must endeavour 
to show that the particles of matter themselves are capable of 
taking up and transmitting the wave-motion. 


Difficulties in the Conception of the Ether. 


The difficulties which one meets with in the belief in the 
existence of this substance may be divided into two classes— 
those founded on theoretical considerations, and those founded 
on experimental evidence. We will first consider the former. 

In the preceding portion we have stated that the ether must 
possess enormous elasticity and very little density. This is 
the view usually accepted: thus Tyndall says, “it is assumed 
to be of both extreme elasticity and of extreme tenuity.”” Now, 
if this be the case, it of course follows that this ether will be 
distributed in space in the same way that matter is distributed ; 
viz. it will accumulate around the celestial bodies, and the 
greater the mass of the body the greater the atmosphere (if 
we may use the term) of ether surrounding it. We ought, 
therefore, to find that a gradual increase of refractive power 
occurred as we approached a celestial body. In the compa- 
ratively few cases in which this can be tested it is found to be 
the case; but it is, I believe, universally attributed to the in- 
fluence of the atmosphere. But we must consider this tenuity 
to be so great that it is impossible for us to recognize it by 
any of our balances. For if we carefully weigh a piece of a 
transparent substance, such as glass, and then grind it to 
powder (in which process we must liberate some of the ether 
which is held between the molecules), and weigh the powder, 
we obtain the same weight as before, showing that the ether 
we have lost had not sufficient weight to affect the balance. 
Some of the upholders of the undulatory theory, however, take 

EA 


228 Mr. H. H. Cook on the Existence of 


a different view: thus Sir John Herschel says, “ though we 
suppose the ethereal molecules to possess inertia, we cannot 
suppose them affected by the force of gravitation.” If this be 
the case, this hypothetical medium has no analogue in nature ; 
it is a substance of which we can form no notion, as it is im- 
possible to conceive a body possessing moving force but no 
weight. Are we not inventing too much when we endow a 
hypothetical substance with impossible properties? Itis curious 
to observe how the same philosopher, in advancing arguments 
against the corpuscular theory, says, “ This is one of the many 
weak points of the theory. Jt runs counter to the only ana- 
logy which the observation of nature furnishes” *. Yet eight 
pages further on he endows the ether with a property which 
causes it to be like no other substance in nature! Again, if 
the ether has no density, itis not necessary for us to assume it 
to possess a high elasticity ; for any value given to the elasti- 


city will fulfil the conditions of the equation o=a/ > In 


fact, the equation has no meaning if v, e, ord=0. We have 
thus arrrived at these conclusions :—first, if we suppose the 
ether possesses weight, we ought to find an increase in re- 
fracting power near large masses ; and, secondly, 1f we suppose 
the ether to be unaffected by gravitation, then it is a body 
which bears no resemblance to any other body we know of. 

Again, the ether is supposed to pervade all bodies, to inter- 
pose itself between the molecules, and, moreover, to be affected 
by the grouping of these molecules. When light passes from 
one body into another, it does so by throwing the ether con- 
tained in that body into vibration. Refraction occurs because 
the elasticity of the ether in the second body is different from 
the elasticity of the ether in the first. But why is this elas- 
ticity different? Weare told because the molecular arrange- 
ment is different in one body to what it is in another ; but are we 
to suppose that the proximity of the ether to different modes 
of molecular grouping causes that ether to be of different 
elasticity ? If this be so, we have to attribute to the ether a 
property which is peculiar to it, viz. that of having its elasti- 
city altered by its proximity to different molecular groupings. 
If we, to avoid this conclusion, suppose that it is the density 
of the ether which undergoes change, then we again make a 
departure from all analogies. We know of no substance whose 
density is altered by the mere presence of another body. 

Nor does it appear that we are better off if we assume the 
ether to be imprisoned between the molecules. For in this 


* Familiar Lectures, p. 269. - 


the Luminiferous Ether. 229 


case, although by the compression we do increase the density, 
yet we increase the elasticity in the same proportion, and 
consequently the velocity remains unchanged. Also, if we 
adopt this view, we must have the entire surface of a body 
composed of its own molecules: there must be no spaces; or 
the imprisoned ether would escape and assume the elasticity 
and density of the ether of the surrounding body. We thus 
arrive at the conclusion that, for refraction to be accounted for, 
we must assume that the elasticity of the ether is different in 
different bodies, and that this difference is due to the proximity 
of the ether particles to the different molecular arrangements 
of bodies. In this assumption, it is needless to state, we make 
a departure from all known facts. We know of no substance 
whose elasticity is altered by the proximity of another body. 
Slightly altering the words of Sir John Herschel, if we accept 
this explanation we are running counter to all the analogies 
which the observation of nature affords. : 

Again, although the ether in a certain sense is a most pow- 
erful substance, capable of entering into all bodies, and of 
vibrating with enormous velocity, yet chemically it is a most 
inert substance. In no way can we cause it to chemically 
combine with any other body. Although in intimate con- 
nexion with the molecules and atoms of all, it chemically 


affects none. In this property, also, our hypothetical medium 


is peculiar ; no substance in nature refuses to combine with 


some one or more other substances. 


The difficulties which one experiences in accepting the 
ether, owing to certain experiments, are varied and nume< 
rous. We will consider some of these. A common experi- 
ment in acoustics is to place an alarm under an exhausted re- 
ceiver and to receive no sound when the air is withdrawn. 
This simple experiment is difficult to explain ; for we must re- 
member that, although the air is withdrawn, the ether remains. 
Why does this ether not take up the vibrations of the sounding 
body and transmit them? It cannot be because the vibrations 
producing sound are too slow ; for an unlimited elastic medium 
is capable of vibrating in any way. The water of the ocean trans- 
mits along rolling wave as readily as the minutest ripple, and 
the minutest ripple as easily as the shortest sound-wave. It will 
not suffice to say that the ether does take up the vibration and 
carry it on to the sides of the receiver, but that here it is unable 
to throw the molecules of the glass into vibration, and hence 
the sound cannot reach the external air, because according to 
theory the.ether is contained in the glass. There is, in fact, 
no break in the line of communication of the ether. particles 
outside with those in the inside of the receiver. What pre- 
vents the vibrations being taken up and transmitted ? 


230 Mr. E. H. Cook on the Existence of 


Another experiment which seems difficult of explanation is 
that it is impossible to cause the electric discharge to occur in 
a perfect vacuum. LHther is present in this case also; yet this 
ether is unable to transmit the electricity. Whatever this 
electricity may be, it is certainly something which is much 
like light and heat, it is therefore probably molecular motion 
of some kind. If molecular motion, our ether ought to be 
able to transmit it ; as it does not do so we are left to choose 
between two alternatives—either to say electricity is not due 
to molecular motion, or that no substance of the nature of 
ether is present. Hvidence seems to be accumulating to show 
that electricity is due to molecular motion ; and we must there- 
fore conclude that no ether is present. 

Thirdly, let us consider Faraday’s experiment with the “ heavy 
glass.””, When a polarized ray is passed along the axis of a prism 
of a transparent substance which under ordinary conditions is 
optically inactive, and the prism placed in the magnetic field, 
then the substance becomes able to turn the plane of polarization. 
Thus, if a polarized ray is sent through a prism of this glass which 
is placed between the poles of an electromagnet, the plane of 
polarization is immediately turned. The reason assigned for 
this peculiar action by Faraday is that the magnet has caused — 
a temporary difference in the molecular constitution of the 
substance ; and he finds that any cause which impedes the 
development of this power of rotation also impedes molecular 
displacement. But Faraday does not commit himself to the 
statement that this alteration of molecular grouping causes an 
alteration in the constitution of the ether of such a character 
as to cause it to vibrate in a particular plane. He simply 
states that a molecular rearrangement has produced the effect, 
and evidently considers this a sufficient explanation. . 

Two observations recently made are also difficult of expla- 
~ nation on the ethereal theory, viz. the increase of the electrical 
resistance of selenium by its exposure to light, and Dr. Kerr’s 
experiments with the light reflected from the polished pole of 
a magnet (see Phil. Mag. May 1877 and March 1878). In 
the first of these we find that the vibratory movement of light 
affects the material particles of matter ; for we believe that the 
particles of the body are alone concerned in the transmission of 
electricity. This difficulty may be overcome by assuming 
the ether to be the medium for the conduction of electri- 
city as it is of light; but up to the present, I believe, this 
theory has not been propounded. Dr.. Kerr finds that the 
light reflected from the polished pole of a magnet is polarized. 
We must therefore suppose that the ether is susceptible of mag- 
netic influence. May I ask if it contains the two magnetic 


the Luminiferous ther. — 231 


fluids? If, however, we consider the particles of the air con- 
cerned in the propagation of light, we have to make no fresh 
assumption, as we already know nitrogen to be very feebly 
diamagnetic and oxygen paramagnetic. The particles of these 
gases are affected by contiguity to the pole of the magnet; 
and this kind of affection is such as to cause the molecules to 
vibrate in certain planes: hence the light is polarized. 

Finally, let us look at the explanation offered by the ether 
theory to two of the chemical actions of light as representa- 
tives of most of the chemical effects of light. We will take the 
reduction of silver salts and the decomposition of CQ, into its 
elements by the action of light on the chlorophyll of plants. 
Scheele discovered that when chloride of silver was exposed to 
light, a black powder, insoluble in nitric acid, was formed ; 
and at the same time free hydrochloric acid was produced. 
The black powder he concluded to be metallic silver. He also 
made the important discovery that the violet rays were far 
more active in-producing this reduction than the other rays. 
Here, then, we have three distinct results to account for, viz.:— 
1st, the production of the black powder; 2nd, the formation 
of hydrochloric acid ; and, 3rd, the superior power of the violet 
rays. The ether theory says that the vibration of the ether 
shakes asunder the bond of chemical union; that is, the 
vibrations of the medium in which the molecules of the ar- 
gentic chloride are imbedded causes the separation of the atoms 
of the molecules. This explanation seems at once insufficient 
and unnecessary. It is insufficient for this reason: it does 
not seem probable that the vibrations of an intermolecular 
medium should be able to cause an atomic separation. It is 
quite possible to conceive that the molecules are caused to 
vibrate by the vibrations of the surrounding ether; but that 
the individual atoms of these molecules are caused to vibrate, 
and that with different velocities, or otherwise no separation can — 
occur, seems improbable. ‘That this vibration of the atoms 
may occur it is necessary to assume that the ether is inter- 
atomic instead of intermolecular. If we make this additional 
assumption, we stretch to the point of breaking an already 
“elastic’’ theory, and we render much more difficult of expla- 
nation the combination of bodies produced by the action of light. 
The above explanation seems unnecessary, because we have 
only to assume that the atoms of bodies are capable of vibrating 
at a great velocity to account for these experiments in a simple 
and most satisfactory manner. The latter portion of this paper 
is devoted to the working-out of this assumption. 

Continuing our investigation of this experiment further, 
we notice that colourless chloride of silver has been converted 


232 Mr. H. H. Cook on the Existence of 


into a black substance. A body is colourless because the power 
of the ether between its molecules to vibrate is the same . 
as the power of the ether in the surrounding medium to 
vibrate. A body is black because its ether takes up and re- 
tains all the vibrations which fall upon it. Thus the vibration 
of the ether in the black substance must be more powerful 
than in the colourless. (This also follows because energy cannot 
be destroyed by the black substance.) Here, then, the vibra- 
tion of the ether in the colourless chloride of silver has pro- 
duced a substance containing ether particles vibrating with 
more energy. In other words, the energy of the vibration in 
the argentic chloride has been used up in first shaking the 
atom of silver from the atom of chlorine, and also in causing 
the ether in the silver and the ether in the chlorine to vibrate. 
According to the conservation of energy, these energies should 
be equal. But we find that there is more energy in the black 
silver than in the chloride ; and consequently we have inequa- — 
lity. 

The reason assigned for the superior energy of the violet 
rays is simple and satisfactory if we admit the previous as- 
sumptions. It is that in consequence of their more rapid vi- 
bration they are more energetic and thus capable of doing more © 

work. 

In the decomposition of carbonic anhydride effected by light 
in the presence of chlorophyll, we have another experiment 
which is difficult of explanation on the ether theory. The 
vibration of the ether of the carbonic anhydride is unable to 
effect the decomposition itself; but when brought near to the 
vibrating ether of the chlorophyll, the decomposition is effected. 
What is the nature of the action which here takes place? and 
what known action is analogous to it? 

Stating briefly the difficulties in the conception of the ether, 
we have :— 

(a) The want of any direct evidence. 

(8) The fact that no ethereal condensation is observed 
around the celestial bodies. 

(y) The interposition of this substance between the mole- 
cules of bodies. 

(6) The nature of the action producing a difference of elas- 
ticity or density in this imprisoned ether. 

(e) The chemical inertness of the ether. 

In addition to these we have from experimental evidence 
the following :— 

(a) Inability of the ether to take up every species of vibra- 
tion. 

(8) Inability to transmit electricity. 


the Luminiferous Ether. 233 


(y) Inability to explain circular polarization produced by 
_ magnetic action. 

(6) Incompleteness of explanation offered of the chemical 
effects of light. 

Probably a more exhaustive survey will reveal other and 
greater difficulties ; but these will be sufficient to show that the 
acceptance of the theory is beset with difficulties and makes 
such great calls upon our imaginations that it behoves the 
least sceptical to “ pause and consider.” 

Now let us proceed with the second portion of our subject, 
to endeavour to show that the particles of matter themselves 
are capable of taking up and transmitting the wave-motion. 
Dalton considered all bodies to be composed of atoms, which 
atoms are all of the same size but of different weights. This 
difference in weight is expressed in the atomic weight of the 
elements. Atoms in the free state combine with each other and 
form molecules. About the absolute size or density of these 
atoms we know nothing, save that they are very very small. 
Recent advances in scientifictheory have but extended Dalton’s 
hypothesis. Thus, a high authority, stating the theory at pre- 
sent held of the constitution of bodies, says :— 

“ All bodies consist of a finite number of small parts called 
molecules. Hvery molecule consists of a definite quantity of 
matter, which is exactly the same for all the molecules of the 
same substance. ... . A molecule may consist of several di- 
stinct portions of matter held together by chemical bonds, and 
may be set in vibration, rotation, or any other kind of relative 
MIOUCHS J... The molecules of all bodies are in a state of 
continual agitation. The hotter a body is, the more violently 
are its molecules agitated’’*. Here, then, heat is produced 
by the vibration of the molecules of bodies. If the particles 
of a body are capable of such rapid vibration in the production 
of heat, why may they not be capable of taking up this vibra- 
tion and transmitting it? It is more than probable that heat — 
is thus transmitted. Why may not light be also thus trans- 
mitted? We only have a difference in quantity between the 
two, heat being produced by the less rapid and light by the 
more rapid vibrations. Nor is the difference so great between 
the vibration producing heat and that producing light. The 
maximum heating effect of the spectrum occurs at a point 
where the rate of vibration is about 400 millions of millions 
of vibrations per second ; the maximum chemical effect occurs 
where the rate is about 800 millions of millions per second. 
As an effort of the intellect, it is as easy to endow matter with 
the ability to vibrate at the latter rate as at the former ; and if 
* Maxwell, Theory of Heat, p. 306. 


234 Mr. H. H. Cook on the Existence of 


it can vibrate at this rate (which seems to be admitted) why 
cannot it transmit this vibration ? 

It cannot transmit it because its densilgat is too great and its 
elasticity too small we should be told. But if we reduce the 
size of the atom we reduce the weight of it, and we reduce the 
amount of energy necessary to throw it into vibration. In 

fact, if we reduce the size 954,188,240,000 times, we should 
reduce the weight and endow the atom with power of vibra- 
ting. It appears, then, that the ability of a body to take up 
vibratory motion depends upon the size of the atom ; and, given 
that the atoms and molecules of bodies are sufficiently small, 
they are capable of transmitting light and heat. In order to 
compare the velocity with which light travels with that which 
sound travels, let us take a few examples. In air we have 
already seen that light travels with 888,500 times the velocity 
of sound. In water we know that sound travels at about 
5000 feet per second. ‘The index of refraction of water is, 
according to Brewster and Wollaston, 1°336 ; if the velocity of 
light in air is 185,000 miles per second, the velocity in water 
is 188,500. Thus the velocity of light in water is 146,300 
times that of sound. ‘The greatest velocity of sound in 
any substance is through iron at 100° C., in which it is 
17,500 feet per second. The substance with the greatest re-— 
fractive index is chromate of lead=nearly 3. The velocity of 
light is therefore less in this body than in any. Let us com- 
pare these two, and we find that the velocity of light in chro- 
mate of lead is only 17,620 times as great as the velocity of 
sound through iron. Now we have no doubt that the sound is 
transmitted through the iron by the vibration of its molecules, 
. why may not the light be transmitted through the chromate of 
lead by the vibration of its molecules ? Here, again, itis merely 
a question of degree ; the one is a more rapid motion than the 
other. There is another point which must not be overlooked in 
comparing sound and light; and that is, that the vibrations of 
the molecules composing a light-wave oscillate in planes per- 
pendicular to the direction of propagation of the wave, while 
those composing a sound-wave oscillate in the direction of pro- 
pagation. This difference, it seems reasonable to suppose, will 
exercise an important influence on the relative velocities even 
in a homogeneous medium. It is evident that it must. do so 
in a medium whose elasticity is different in the two planes, 
a. €. the plane of propagation and the plane of vibration. 

And in thus assuming that the particles of matter themselves 
are capable of vibrating : and propagating the undulatory move- 
ment of light, are we making too great a strain upon them ? 
Certainly not. We can form no notion, even the most remote, 


the Luminiferous Ether. 235 


of the magnitude of these particles. The best microscopes will 
detect particles saan of an inch in diameter; yet “ we are 
here dealing with infinitesimals, compared with which the test- 
objects of the microscope are literally immense”’*. By means 
of the spectroscope we can detect somos of a grain of sodium ; 
so that the atom of this metal must be smaller than this. Also, 
‘‘ the number of molecules in a cubic millimetre of atmospheric 
air is about a unit-eighteen (10'*)”’ t—that is, one million 
billions! (A billion is a million times a million.) With a 
wave-length of =, of a millimetre, we cease to have any lumi- 
nous effect, but we still possess a faint photographic effect. 
We therefore see that the shortest waves in the spectrum are 
of immense length when compared with the size of the mole- 
cules of a body. With regard, then, to the size of the mole- 
cule, we can have no doubt that it is sufficiently minute to 
be fully able to oscillate and produce waves of the size of those 
of light. But can these molecules oscillate with sufficient 
rapidity ? In an article on “ Polarization Stress in Gases ”’ 
(Phil. Mag. Dec. 1878), Mr. G. J. Stoney supplies data which 
will enable us to answer this question. At common tempe- 
ratures the average velocity of the molecules of air may be 
taken as 500 metres per second. The molecules meet with so 
many encounters that the direction of the path of each is 
changed 10,000,000,000 times a second. We have, then, that 
in one movement the particle travels om of a metre, or 
xz» Of a millimetre; and it makes this movement in ina 
of a second. Now we have seen that the length of the 
waye of the extreme chemical ray is =, of a millimetre; con- . 
sequently we find that the molecule of air travels through a 
distance which is more than twice as long as the length of this 
particular wave in this fraction of a second. The time of one 
oscillation of the molecules composing the mean chemical rays 
may be taken as S00 000 000,000 of a second. ‘Thus, in 80 times as 
long as the time occupied by a molecule in one oscillation the 
molecule of air has travelled through a distance twice as long 
as that of the whole wave-length. ‘The distance moved through 
by a wave would be underestimated at a million times the 
distance moved through by a molecule composing that wave ; 
consequently we see that our air-particles move with a far 
higher velocity than that required by the shortest waves of the 
spectrum. 
* Tyndall, ‘Scientific Use of Imagination,’ p. 25. 
t+ Johnstone Stoney, Phil. Mag. December 1878, 


236 Mr. E. H. Cook on the Emistence of 


With these considerations before us, what need is there to 
assume the existence of an all-pervading ether? The particles 
of ordinary matter are small enough, and can, nay do, vibrate 
at the requisite speed; why, then, are these particles not able 
to transmit the waves of light? Substituting for the lumini- 
ferous-ether theory this molecular theory, let us now see if the 
explanation of some of the difficulties of the former theory are 
satisfactorily accounted for. Before doing so, however, I will 
endeavour to answer two objections which it seems to me may 
be made against this theory. First, it may be asked, If light 
travels through bodies by the vibrations of its molecules, why 
is not the velocity of light through the body the same as the 
velocity of sound? In answering this we must bear in mind 
the differences between sound and light. The shortest wave 
of sound would be produced by 38000 vibrations per second, 
and would have a wave-length of about 9 millimetres, or 11250 
times as great as the length of the longest wave of light. We 
have also to remember that the particles of a sound-wave os- 
cillate in the direction of propagation, whilst those in a light- 
wave oscillate in planes perpendicular to that of propagation. 
Is it unreasonable to suppose, then, that so vast a commotion 
as that produced by sound in the direction of propagation should 
be retarded more than the minute disturbance produced by 
light in planes at right angles to this direction? Another ob- 
jection which may be urged is, How do we account for the 
motion reaching us from the sun? We may do this in two 
ways: first, we may fill the space between the sun and earth 
with the luminiferous ether, and give this ether the property 
of non-miscibility with the atmosphere ; or, secondly, we may 
assume the unlimited extent of our atmosphere. Hither of 
these assumptions would be sufficient to account for the phe- 
nomena; and both have before been made. 

Let us now see if these difficulties we have mentioned in 
regard to the conception of the ether are lessened if we con- 
sider the particles of matter to vibrate. It is evident that a 
condensation of matter does occur around the celestial bodies, 
and also that a gradual increase of the refractive power occurs 
as we approach large masses. We have here no difficulty in 
conceiving the cause of the difference in the refractive powers 
of bodies ; it is simply due to the different density of the bodies 
and to the mode of grouping of the molecules interfering with 
perfect freedom of motion of these molecules. A glance at 
what may be termed the experimental difficulties given above 
will suffice to: show the ability of this theory to satisfactorily 
account for these experiments. 

Numerous experimental facts support this assumption in an 


the Luminiferous Ether. 237 


indirect manner. For instance, the greater the atomic weight 
of the substance the greater ought to be the refractive power 
or the less the velocity in the body. Unfortunately, how- 
ever, this rule cannot be generally applied, because of other 
conditions which prevent the free motion of the molecule. 
But we know that in the gaseous condition the molecules are 
less hampered than in the liquid and solid states ; the refrac- 
tive indices of gases ought therefore to exhibit some increase 
with the density. The following are the indices of refraction 
and densities of the five simple gases :— 


Refractive Power. . 


Gas. ee Ginted Density 
x with Air. 
Hydrogen ...... 1000138 0-470 0-069 
Nitrogen ...... 1:000300 1-020 0-971 
BP guano 1000294 1-000 1-000 
Oxy Benly nce nides 1-000272 0:924 1-106 
Chlorine ...... 1000772 2°623 2-470 


And it will be seen that, with the exception of oxygen, this 
fulfils the condition mentioned above. But the position of 
air is most instructive : it is seen that, like its density, its re- 
fractive power is intermediate between that of its constituents. 
What stronger indirect evidence than this can we have that 
the velocity in a medium is due to the density of the molecules 
of that medium ? 

A further examination of this list is of value. We notice 
that oxygen is an exception. Now the other three gases are 
what chemists call monads; oxygen, on the contrary, is a 
dyad. The molecule of oxygen, let us assume, consists of one 
atom, while the molecules of H, N, and Cl consist of two. 
Altering, then, the density of oxygen to one half that given, 
we find it occupies its proper place in the list. The following 
table exhibits this and other relations :— 


a Density of leg: RE anna Riot Refractive Power. Air=1. 
Molecule. | Density. aie li 
~~" | Caleulated. | Observed. 
Hydrogen 2 1-414 1 ‘470 ‘470 
Oxygen ...... 16 4-000 28 13160 924 
Nitrogen ... 28 52915 o7 1-7390 1:020 
Chlorine .. cal 8-426 59 2°7730 2°623 


* Other considerations lead us to consider that the molecule of O con- 


sists of two atoms; if this be so, we must consider O an exception. 


238 Mr. E. H. Cook on the Existence of 


It is impossible not to be struck with the relation which is 
here exhibited, especially when we remember how many in- 
fluences are at work interfering with the perfect freedom of 
motion which is necessary for this law to be rigorously true. 
Numerous confirmations of this molecular theory occur when 
we examine tables of the refractive indices of various bodies. 
We extract the following passages from the article “ Light” 
in ‘ Watt’s Dictionary of Chemistry,’ vol. 11. pp. 616-618 :— 

“‘ Generally speaking, the refractive power of any one sub- 
stance increases with its density.” . 

“The refracting power of liquids is diminished when they 
are expanded by heat.”’ 

Biot and Arago ‘‘ found that at pressures not exceeding that 
of the atmosphere, the quantity ~”—1, which is called the ab- 
solute refractive power, is proportional to the density of the 

as.” 

“ Dulong has shown that the refractive power of a mixture 
of gases is equal to the mean of those of the constituent gases 
calculated for the pressure to which each gas is actually sub- 
jected in the mixture.”’ 

Compare the self-evident explanation offered of these results 
on the molecular theory with the complicated and unsatisfactory 
nature of that afforded by the ether theory, even after assuming 
the existence and all-pervading properties of this substance. 

Again, in the complicated phenomena of interference and 
polarization, how few are the assumptions which we have to 
make! No difference in elasticity of a contained medium, 
owing to the different molecular groupings, but these diffe- 
rent molecular groupings themselves all-sufficient to account 
for the phenomena. 

Colour and chemical action are also found to be very much 
more easily explained, when we consider the molecules of 
bodies to vibrate instead of the molecules of the ether. 

Summing these conclusions, we have :— 

a. The molecular theory makes no departure in its assump- 
tions from the analogies observed in nature. 

8. The phenomena of refraction follow as a consequence of 
this theory. 

y. The complicated phenomena of colour, double refrac- 
tion, polarization, and interference are all explained without 
ne assumptions which have no analogies in observed 

acts. } | 

6. Independent phenomena, especially the increase of the 
refractive powers of gases with the increase of their densities, 
support this theory. 

«. The turning of the plane of polarization by the passage 


the Luminiferous Ether. 239 


of light through various substances placed in the magnetic 


field follows as a consequence of the influence exerted by the 
magnet on the molecules of the body. 

In conclusion, in the following Table is drawn up a compa- 
rative view of the explanations and assumptions made in the 
two theories of the various phenomena of light. 


Phenomena. Hther Theory. Molecular Theory. 
Light is transmitted by the |} Light is transmitted by the 
Je vibrations of an elastic and vibrations of the mole- 
eee all-pervading medium. cules of bodies. 
The elasticity or density of | \ 
| 


the ether is altered by its} | The molecules of different 


Refraction contiguity to the mole- bodies move with diffe- 
cules of the refracting rent degrees of freedom. 
body. 

: with different degrees of : 

oa velocity for dition co- oe for some colours 

ine an for others. 
The impact of the ethereal 
waves causes the ether in The j 

Calorescence the bodies to vibrate, e impact of the molecular 

and. sometimes with greater, waves causes the. mole- 

fluorescence. sometimes with less velo- cules of the bodies to vi- 


city than the particles of brate. 


ether in these waves. 
The oscillation of the mole- 
cules of the radiating body 


throws the particles of | | The molecules of the radi- 


ether in the surrounding 
medium into vibration. 
This vibration causes the 
_| ether in the absorbing 
body to vibrate; and the 
vibration of this ether 
causes the molecules of the 
absorbing body to vibrate. 
Owing to the different group- 
ing of the molecules of the 
Double refrac- 4 erystal, the elasticity or 
CHI. +3i.4050 S00 || density of the ether in 
|| which these molecules are 

contained is altered. 


Radiation and 
absorption... 


the molecules of the 
body are contained shakes 
these molecules, so as in 
one case to overcome the 
bond of chemical union be- 
tween the atoms of the 
molecule, in the other case 
to cause the atoms to com- 
bine. 


MCHON, x. cues 


| 
Chemical | 
| 

K 


4 P 
| 
{| ether particles vibrate e molecules vibrate more 
| | 
| | 
\ ) 
| | 
4 


eee +> Oo Or 


| 


ating body vibrate; this 
throws the molecules of 
the surrounding medium 
into vibration ; and these 
throw the molecules of 
the absorbing body into 
vibration. 


The freedom of the mole- 


cules to vibrate is diffe- 
rent in different planes, 
owing to the molecular 
constitution of the erys- 
tal. 


The vibration of the mole- 


cules of the body causes 
in one case the force of 
chemical affinity to be 
suspended ; in the other, 
it causes the force to be 
brought into action. 


[ 240 ] 


XXXIX. On the Modulus of Cohesion of Ice, and its bearing 
on the Theory of Glacial Erosion of Lake-Basins. By R. 
D. OLDHAM™*. 


(arate advantage of the late frost, I was able, through 

the kindness of Mr. Hall, the manager of the Victoria 
Lime and Cement Works, Rugby, to make a series of experi- 
ments with a view to determining the modulus of the cohesion 
of ice, so as to be able (reasoning from that) to determine 
whether it would be possible for a glacier to scoop out a lake- 
basin of any considerable size. 

Before describing the results of these experiments, it may be 
well to mention the mode in which they were conducted. The 
machine used was an ordinary cement-testing machine, which, 
as used by me, was arranged as a simple lever of the second 
order multiplying five times. From the nature of the machine, 
it was impossible to arrange for a perfect counterpoise ; nor, 
with the instruments at my disposal, could I make any accu- 
rate determination of the initial pressure on the test; but I 
was able to estimate it as not far from 20 lb., which I have in 
each case added to the pressure indicated, in order to obtain 
the full pressure on the test. The samples experimented on 
were frozen in cubical moulds of 14 in. in the side, and were 
for the most part perfectly clear and transparent, though just 
in the centre they were sometimes more or less opaque. As, 
however, this opaque portion was never more than 4 inch in 
diameter, the error so introduced is insignificant ; and as the 
specimens were exposed, in their frozen state, to temperatures 
never rising above freezing-point for periods varying from 4 
or 5 to over 24 hours, there could be no interstitial moisture 
which would vitiate the results. 

A few words in description of the behaviour of these samples 
of ice when subjected to increasing pressures may not be amiss. 
As the pressure was applied, the ice did not seem to yield at 
first ; but as soon as the pressure reached about 150 lb. on the 
square inch, very evident signs of yielding showed themselves: 
first a crack would form in one part of the cube, the sides of 
which would slip over each other a little and then unite again; 
the same process would be repeated elsewhere, and then again 
somewhere else; so that, by a continuous giving way and 
reuniting, the ice would yield indefinitely to this pressure, 
though it would not actually crush. It is the pressure at this 
point which .is noted in the Table below as the pressure at 
commencement of yielding—not because I believe that no 


* Communicated by the Author. 


Mr. R. D. Oldham on the Modulus of Cohesion of Ice. 241 


pressure less than this could produce any change of shape in 
the ice (for I feel sure that, if continuous for an indefinite 
period, a pressure far less than this would be sufficient to pro- 
duce an indefinite change of form), but because, from the 
nature of the case, any such slow and gradual yielding could 
not be detected, both on account of the warmth of the testing- 
room and the small range of motion allowed by the machine, 
while the pressure at which the ice began to yield by the con- 
tinuous formation of small cracks could be comparatively 
easily determined with sufficient approach to accuracy. 

As the pressure was increased the yielding went on faster 
and faster, till when a pressure of about 400 |b. on the square 
inch was reached the ice could no longer yield in this conti- 
nuous manner, but was crushed to pieces. The pressure at 
this point is noted in the fourth and fifth columns of the 
Table below:— 


Pressures. 


For commencement of ROn Geuahen 
yielding. 8: 
Pounds per) Modulus, |Pounds per| Modulus, 


squareinch.| in feet. |squareinch.| in feet. 


I ena e | yaa cs. 354'5 869 
Soo A ile ie oe a aR 457°8 1122 
EE cei ass [oy “bSeaay 369 904 
. A, 121:5 MM A eae alaitartah Wy MN ies aide ale 
B. 153-4 ued dan Bat Ren (lated I Not caushed: 
6. 164°5 403 457°8 1122 
if 153-4 376 357°8 877 
8. 164°5 403 307'8 877 
Average ..| 151°5 371 392-4 960 


The above Table shows that, under a pressure of a column 
of its own substance 370 feet in height, ice must yield, and 
that no slow pressure greater than one equivalent to that depth 
of ice could be transmitted by ice, while under a pressure of 
960 feet of its own substance ice would be crushed; but, to 
prevent any error on the wrong side, I shall take the modulus 
of ice at 1000 feet, or nearly three times what was actually 
observed. 

In order to apply these figures to the investigation of how 
far it would be possible fora glacier to scoop out a lake-basin 
of any considerable size, it will be necessary to form some idea 
of what is the friction between the base of a glacier and its 
bed. Now on this point we have, fortunately, experimental 
evidence ; for the angle of repose of clean ice on moderately 


Phil. Mag. 8. 5. Vol. 7. No. 48. April 1879. U 


942 Mr. R. D. Oldham on the Modulus of Cohesion of Ice. 


rough sandstone has been determined by Mr. Hopkins* to be 
20°. Now, as the base of a glacier has imbedded in its sub- 
stance quantities of rock (for, if not, there could be no erosive 
power), the coefficient of friction must be greater than tan 20° 
or 577. In the following calculations I have taken it at only 
‘2, so that there shall be no chance of exaggeration. 

The next point to be determined is, what pressure acting 
parallel to the surface of the bed would be required to force a 
glacier en masse through and out of a lake-basin which it had 
filled in its onward course. In the figure let gg represent a — 


| 6 

glacier flowing over its bed dabce, and let abc represent the 
longitudinal section of a rock-basin which it has filled: it is 
required to determine the lowest pressure which will cause 
the prism bc¢ ki to be forced up the inclined plane bc. Then 

P=wsin 6+ pw cos 8, 
where P is the pressure, expressed for convenience in vertical 
feet of ice, w the weight of the prism, » the coefficient of re- 
sistance, and @ the angle of the slope bc. In this equation 
w sin 8 is constant; for w varies as cosec 0, and is always equal 
to the resistance due to a column of ice in height equal to the 
depth of the lake-basin, which may be called D; and since 
w sin @=D, wwcos @ will equal wD cot @; so that the equation 
becomes 

P=D+2D cot 6, 

or P=D(1+pcot@). 37a sees 
Thus P increases approximately as cot 0. 


* Quoted by the Rev. T. G. Bonney, M.A. (Quart. Journ. Geol. Soc, — 
vol. xxvii. p. 322, 1871). 

+ Inasmuch as a glacier could not (if a rigid body) flow down an angle 
of less than 20° by its own weight, and as the upper surface of glaciers is 
known to move when the inclination is much less, it is evident that the 
resistance of ice to change of shape cannot be very great, or, in other 
words, that under a comparatively small pressure it apparently behaves 
as a viscous body. But this does not affect the question of whether the 
base slides over its bed: if the angle of slope be but 5° it could not, 
though that might be an angle sufficiently steep to allow the upper 
portions to slide over the lower. 


Mr. R. D. Oldham on the Modulus of Cohesion of Ice. 248 


Ti will be necessary also to determine what is the greatest 
pressure which could be transmitted by the prism bck. This 
is governed partly by the modulus of cohesion of the ice, and 
also by the extra support given by the excess of thickness of 
the ice over 6 compared with that over c. Giving this its 
utmost power, 
eae ey, wwe CEE) 
where 

Q = the ultimate strength of, or the maximum pressure that 

could be transmitted by, the prism bce ki, 

m = the modulus of cohesion, 

x == the thickness over 0, 

y = the thickness over c. 


But it is evident that if P is greater than Q, or, in other 
words, if the pressure required to overcome the resistance is 
greater than the utmost pressure that can be transmitted, no 
motion as a whole can ensue, and consequently no abrasion of 
the bed bc can take place ; so that for given values of 0, 2, y, 
and mw, D attains its maximum when 


P=Q, 


or 
m+a—y=D(1+ cot §), 
or , 
_ m+a-y . 
Warr: coke : pe CER) 


In the above equations the pressure has been supposed to 
be limited, in the first case, only by the resistance to be over- 
come, and in the second by the ultimate strength of the ice. 
But if the slope of the bed of the lake-basin from a to 6 is less 
than the angle of repose—that is (taking § as the angle of 
slope), if tan @ is less than yw, the ice cannot slide down of its 
own weight, but must be pushed down ; and consequently the 
actual pressure exerted at b could not equal Q, but would be 
diminished by a quantity equal to that due to the resistance 
to motion down ab. Here the same equations as before hold 
good, substituting —6 for @, 


S=wsin —6+pwcos —6; 
or 

S=pw cos B—w sin B; 
or 


SS Difupahte). wcis uh as wk oe CW) 


But the total pressure which could be transmitted at a only 
U2 : 


944 Mr. R. D. Oldham on the Modulus of Cohesion of Ice. 


equals m; so that the total depth to which a glacier could be 
forced down a slope is 
m 
Dir fe cot B— 1 
Or if » represent the thickness of the glacier at the head of the 
slope, and v that atthe lowest point to which it can be forced, 
oe OS Commas i 
sobp=1' |) (V.) 
Suppose T to be the total pressure which, if applied at a, 


would be required to impel the glacier, as a whole, through 
and out of the basin abc; then 


T=P+8 
=D(1+pcot#)+D(ucot8@—1) — 
=pD (cot @+ cot 8). ...«) = 4k) ees 


But as the pressure which can be transmitted at a is only m, 
we get the greatest value for D when 


m=pD (cot @+ cot P), 
or 
™m 


hn p (cot 6+ cot)’ 


supposing the thickness of the glacier at the lower end to be 
the same as that at the head of the lake; but if there be any 
difference, D cannot be greater than 


a ea ale ? 
Ds ae aes Ae ah eS 


z being the thickness at the upper, and y at the lower end of 
the lake-basin. 

As, however, it will not always be necessary or convenient 
to find the maximum value of D, but rather of ab (that is, the 
maximum distance to which motion could be transmitted 
through a glacier as a whole), this may easily be deduced 
from the above formule; for if L represent the extreme dis- 
tance to which motion can be transmitted, then D=L sin @ or 
Lsin 8, as the case may be. Substituting this in (III.) and 


(V.), 


LS We ey 
~ sinéd+ pcos 0’ 7 
or 
CO Uae a (IX.) 


~ 4200s B—sin B 


dl 


Mr. R. D. Oldham on the Modulus of Cohesion of Ice. 245 
both of which, when the slope vanishes, become | 
[ie Sey 5 Sera pee aoaleed 6 5: 


be 
7 being the thickness at the commencement of the level ground, 
and / at the extreme point to which motion could be commu- 
nicated. 3 

I would here call special attention to one point proved by 
the above formule, and which is at first sight totally opposed 
to the idea one might naturally form of what was actually the 
case,—namely, that the resistance which would be opposed to 
a glacier moving as a whole through any depression that might 
lie in its path is shown (by formula V.) to increase as the 
slope leading out of that depression diminishes, and approxi- 
mately in the ratio of the cotangent of the angle of slope: 
thus, for an angle of 1’ the resistance would be ten times that 
for an angle of 10’, for an angle of 10’ about ten times 
that due toa slope of 1° 40’, and for a slope of 5° about one fifth 
that due to a slope of 1°. This is of the greatest importance; 
for wherever the theory of glacial erosion is upheld, especial 
emphasis is laid on the fact that the hollows in which lakes 
are situated are of but insignificant depth compared with their 
length—a fact which investigation shows to be the very point 
that would make the excavation of lake-basins of any great 
size by these means not only improbable but absolutely im- 
possible. 

But as formule, in the state of formule, are distasteful and 
unintelligible to many, I will apply the formule deduced above 
to actual examples; and for this purpose I shall begin by con- 
sidering the case of the Lake of Geneva, as it is the one con- 
cerning which I can obtain the most perfect data, and which, 
through the wide-spread circulation of Professor Ramsay’s 
‘Physical Geography and Geology of Great Britain,’ and 
from the fact that it was selected as an illustration in his 
original memoir, is best known. From Professor Ramsay I 
take the following data :—extreme length 45 miles; extreme 
depth 984 feet, say 1000 feet (for the lake must have been 
at least that depth originally) ; distance of greatest depth from 
lower end 25 miles,—giving a slope into the lake of 33/ and 
out of the lake as 26’, taking both as uniform. 

Now the pressure necessary to force the glacier en masse 
through the lake is, by (VI.), 

T=pD (cot 6+ cot 8). 
Here D=1000, w is taken at *2, cot 0=132°22, and cot G= 
104:17; whence 


T=47,278 ; 


246 Mr. R. D. Oldham on the Modulus of Cohesion of Ice. 


so that it would require a pressure of over 9 miles of ice to 
force a glacier en masse through and out of the Lake of 
Geneva. Compare this with the observed modulus, and further 
comment is superfluous. 

Having thus proved that, in the case of the Lake of Geneva, 
the theory of glacial erosion is inadmissible, it may be well to 
show what is the very largest lake-basin that could possibly 
be scooped out bya glacier. To this end let both 0 and B=5°, 
a supposition more favourable than is found to be the case in 
nature ; then by (VIL), 

nee = Y 

reece? 
Here, taking y as $z and pw as °2, we get the result that a gla- 
cier, 5000 feet in depth at the head of a lake-basin and thinning 
off to 2500 feet at its base, could not scoop out a lake of more 
than 700 feet in depth under any circumstances whatever, nor 
indeed could it scoop out one of even that depth; but I am at 
present only attempting to find a limit to its power. 

One more point. The greatest distance to which a glacier 
could be forced en masse is given by (X.) as 


i eae 
bo 


Here, taking i as 5000 feet and /as nothing, we get L=30,000 
feet, or rather over 5 miles; so that a glacier debouching 
on a plain could not exert any erosive power on that plain for 
more than five miles from the commencement of its level 
course, and consequently could not scoop out a lake-basin of 
more than that length, whatever its depth might be, nor could 
it be pushed over a plain en masse for more than that distance ; 
but if it did extend further, this could only be possible by the 
sliding of the upper over the lower portions of the glacier, by 
virtue of the pseudo-fluidity of ice. ee 

These last figures also show the fallacy of the idea that a 
vast ice-cap*, such as is supposed by some to have covered 
the greater part of Scotland, Ireland, and Wales, and even to 
have extended continuously to Scandinavia, could move en 
- masse over distances measured, not by miles, but by hundreds 
of miles, passing in its onward career over hill and valley, 
mountain and plain, with one general movement’‘of its own, 
totally independent of the shape of the ground over which it 
moved, and everywhere polishing and scratching the rocks 
over which it passed in one general direction—that of its own 


* I owe this suggestion to Mr. R. Mallet, F.R.S. 


Mr. R. D. Oldham on the Modulus of Cohesion of Ice. 247 


motion. Such an ice-cap may have existed, and under favour- 
able circumstances may have had some motion ; but if so, the 
motion was confined to the upper layers, for the lower portion 
must have been landlocked and stagnant. 

This note has already run to some length; so I shali conclude 
by pointing out:—that the figures given above are not meant 
to represent what a glacier actually can do, but the very outside 


limit of what it could possibly do, and, as such, a very large 


discount may be taken from them without altering their truth ; 
that they will hold good on any theory of glacier-motion, for 
the resistances of friction and gravitation will remain ; and 
that the points I claim to have proved are as follows :— 

1. That no lake-basin exceeding 700 feet in depth or 5 miles 
in length could possibly owe its origin to glacial erosion, 
though the true limits are probably not one tenth of these 
quantities. 

2. That no glacier could be pushed en masse over a plain 
for more than 5 miles. 

3. That, consequently, no ice-cap could travel en masse over 
large areas independently of the conformation of the ground 
over which it travelled. 

January 25, 1879. 


PS.—Since writing the above, it has been pointed out to 
me that it is hardly justifiable to apply the formule of rigid 
dynamics to the case of a body like ice, which, when moving 
in large masses, assumes many of the appearances of a liquid 
in motion. I may therefore point out that the idea in the 
above paper is that, as soon as the resistance offered by fric- 
tion rises to that point at which it would prevent all motion in 
the glacier if the glacier behaved as a perfectly rigid body, 
that point gives a limit beyond which it would not be possible 
for any motion of the base of the glacier over its bed to take 

lace. 
: Mr. Robert Mallet authorizes me to state that, according to 
experiments made by Professor Phillips, the modulus of ice is 
reduced to almost nothing by the presence of interstitial mois- 
ture ; so,that if, as is generally supposed to be the case, glacier- 
ice is permeated by interstitial moisture, the power of a glacier 
in scooping out lake-basins would be reduced to almost no- 


thing. 
Rugby, Feb. 15, 1879. 


ja i | 


XL. On the Luminosity of Gases through Electrical Dis- 
charges. Supplement to the Paper on the Nature of Spectra. 
- By EILHARD WIEDEMANN™. 


- an investigation published in this Journal I expressed 
the opinion that by the electric spark, independently of 
the temperature of a mixture of gases, certain particles are 
rendered luminous, and that the luminosity is not a direct 
consequence of a great rise of temperature, like the brightness 
of incandescent solids, for instance, or that of sodium vapour 
in a gas-flame. I have, on that account, compared the phe- 
nomenon in question to the phenomena of fluorescence. 

New experiments have confirmed this view, and yielded the 
result, that a gas may become luminous, on electricity passing 
through it, while yet its temperature is far below 100°. 

For the experiments a discharge-tube was used consisting, 
first, of a wider portion 30 millims. in diameter and 90 mil- 
lims. in length, which was conically drawn out at its ends. 
To one end a glass bulb provided with a glass cock was fused, 
in the middle of which was an aluminium knob, serving as 
electrode ; to the other end a capillary tube bent in the shape 
of a U, diameter 0°854 millim., height of the U about 93 mil- 
lims., was joined by fusion, to which was attached a glass bulb 
with cock and aluminium electrode. 

The U-tube was placed in a calorimeter, which consisted of 
a brass tube filled with oil of turpentine into which a ther- 
mometer dipped, and was enclosed in a double-walled vessel 
filled with water. The waterworth of the entire calorimeter 
inclusive of the oil of turpentine, the thermometer, and the 
immersed portion of the U-tube, amounted in the experiments 
to 8°846 grams. 

The discharge-tube was filled with air and exhausted (to 
about 3 millims.) till the entire wide tube was completely 
filled with continuous light when the discharges passed through 
it. A very feeble stratification appeared momentarily in iso- 
lated cases only. After the pressure was read off, the cock 
communicating with the air-pump was closed. 

A Ruhmkorff induction-coil of medium size, with a mercury 
interruptor, served as the source of electricity. By a simple 
arrangement a black-writer was inserted, through a relais, in 
a second current-circuit, which marked the number of the 
closings of the Ruhmkorff, and therefore also the number of 
the discharges through the Geissler tube. 

* Translated from a separate impression, communicated by the Author, 


from Wiedemann’s Annalen, vi. pp. 298-802. 
t+ Phil. Mag. Feb. 1879, pp. 77-95. 


Luminosity of Gases through Electrical Discharges. 249 


The inductorium was excited by two Bunsen elements. The 
calorimetric determinations were carried out in the following 
manner:—First, for 5-10 minutes before the experiment the 
course of the thermometer was observed ; then, exactly at the 
minute, the primary circuit of the inductorium was closed. 
When with the play of the interruptor a sufficient augmentation 
of the temperature of the calorimeter had taken place, the cur- 
rent-circuit was again opened, at a moment which was read off, 
and the course of the thermometer followed again during 
5-10 minutes. From the rise of temperature which had 
taken place, corrected in the well-known manner, and from 
the number of the discharges, counted on the strip of paper 
of the marker, the quantity of heat generated at each single 
discharge in the capillary tube could be calculated. From 
this, and from the dimensions of the capillary tube, the tem- 
perature of the gas can be approximately ascertained, pro- 
vided that its specific heat does not alter much with the tem- 
perature. 

From the older experiments of G. Wiedemann and the newer 
ones of A. Naccari and Bellati, however, it follows that the 
quantity of heat generated in each cross section ofa discharge- 
tube at the passing of the discharge is independent of the 
magnitude of the section, and in very wide tubes is somewhat 
less. It thence follows, further, that the increments of tem- 
perature must be inversely proportional to the cross section, 
and so the increments of temperature of the gas in the wider 
tube can be calculated from those observed in the narrower 
one. 

If p is the pressure of the gas, V the volume of the heated 
gas in the capillary tube below the surface of the oil of tur- 
pentine, z the number of discharges in a minute, Z the time, 


in minutes, during which the discharges pass through the gas, 


¢ the corrected increase of temperature generated in the calo- 
rimeter, ¢ the specific heat of the gas, s its specific gravity at 
0°, w the waterworth of the calorimeter, then the increment 
of temperature T of the gas, to be calculated from the above 
quantities, at each discharge in the capillary tube is very 
nearly 
pa we: 760, 

VsepZz ° 

* For ¢ I have introduced the specific heat at a constant pressure, 
0:237. It might, however, be possible for the heating in a part, at least, 
of the capillary tube to take place at constant volume; the numbers found 
for T and 7 would then become ¢ higher. In face of this uncertainty the 
error vanishes completely which we have committed in putting for's the 
specific gravity at 0° and not that at the temperature of the experiment. 


250 Luminosity of Gases through Electrical Discharges. 


Dividing T by the ratio of the cross section of the wider 
tube to that of the narrower (1232), we get the increment of 
temperature in the former, 


= 7939" 


Of a whole series of experiments I give the following five, 
together with the values obtained from them for t and T:— 


Vy. 
Dp. Ea Tee Z. Z. te af: i. 
33 | 009774 300 9 3°93 84340 68:0 
33 ; 342 8 3:24 80150 65°2 
33 2 348 8 3°52 85560 69°5 
2°66 A 348 10 351 86660 70-4 
2°66 “ 338 14 4:35 77250 62:0 


As the mean temperature of the gas, before the passing of 
the discharge, amounted to about 20°, the maximum tempera- 
ture generated in the first tube was about 80—90°; and there- 
with the gas was brightly luminous. 

It is necessary to remark that if alternating partial dis- 
charges take place, the above temperature is still too high ; 
and so itis when the discharges do not take place momentarily, 
but last a certain time. Further, since the gas constantly 
becomes quite dark again between every two discharges, and 
shines as brightly after the first as after the later ones, the 
luminous appearances cannot be conditioned by heatings being 
accumulated by the successive discharges. ‘The temperature 
62-70° is at all events not the lowest at which the gas appears 


luminous ; for when the discharges of a Holtz machine were © 


conducted through a discharge-tube precisely similar to that 


above described, the wider part of it appeared completely filled © 


with light, while the light in the narrower part was much 
fainter than when the inductorium was employed. Exact calori- 
metric measurements are, in consequence of the inconsiderable 
production of heat, much more difficult to make with the 
former than with the latter. 

The luminousness of the gas at so low a temperature during 
the passage of electricity proves, when viewed in connexion 
with the mechanical theory of gases, that the eleciric discharge, 
independently of an augmentation of the vis viva of the pro- 
gressive motion of the molecules by temperature, calls forth a 
considerable heightening of the vis viva of the oscillatory 
motion of the ether envelopes. 2 

To make use of the result here found for explaining what 
goes on in the discharges in gases, and the nature of the elec- 


+) Se eal aR Oct eee NA i a GIAO Nae Als Mla Met tpi 


— On Variation of Thermal Conductivity of Metals. 251 


tricity-motion, as well as for the application of electrical dis- 
charges to the study of the spectra of gases, is reserved 
for separate investigations. Meanwhile so much is even now 
evident, that the different spectra in the parts of different 
width of discharge-tubes are not to be referred alone to the 
different temperatures of the gases, but depend essentially 
upon the amounts of electricity the passage of which condi- 
tions the oscillatory motions of the ether envelopes of every 
individual atom or molecule. 

By means of such calorimetric measurements we might in- 
deed succeed in determining the quantities of heat which are 
necessary in order so to alter the state of the molecules and 
atoms that the band spectrum shall change into the line spec- 
trum ; or, in other words, if we adopt the views developed in 
the former paper, we must be able to ascertain the amount of 
heat which is set free at the formation of the molecule of a 
simple body out of its atoms. 

I shall shortly communicate something further upon these 
subjects. 


Leipzig, January 1879. 


XLI. On the Determination of the Variation of the Thermal Con-~ 
ductivity of Metals with Temperature, by means of the perma- 
nent Curve of Temperature along a uniform thin Rod heated at 
one end. By Outver J. Lopez, D.Sc., Lecturer on Applied 
Mathematics and Mechanics at University College, London. 


[Concluded from p. 211. ] 
Introduction of the experimental Values of the Variables into 
Equation (3) and the first Integration of tt. 
16. HAT we haye accomplished so far is:—the writing of 
the fundamental equation (1) by help of equation (2) 
in the form (3), which involves the ratio of rate of cooling 6 to 


thermometric conductivity = and then the expression of these 


two quantities as functions of the temperature—the one as a 
complex function (5), the other as an inverse linear func- 
tion (4). The latter contains Centigrade temperature ¢; but 
if we reckon temperature from the temperature of the enclo- 
sure Uv, instead of from the Uentigrade zero, it will only affect 
the value of the constant 6. So writing 1.+b—274=m, we 
get (4) in the form 

ee on Dei iabe 33 mak 9 

68 CMO ys 6:0) Wa ees ako BS (9) 


252 Dr. O. J. Lodge on the Variation of the Thermal 


Hence the equation (3) may now be written 


20 9 
c= {Pam(a?—1) + Doron, er Ci 


or, say, for shortness, 


LO | 

Fee {R(a’—1)+ Sats (m+6@). 2 Se ee (11) 
This equation has now to be integrated. Whether it can be 
integrated completely as it stands I do not know; but a first 
integration is easy, and the result is 


1/40 po Car 1 Ga 

= = Toga ("+9 igo g) BO pa) = g Ro 
ot ae ay 

Se CE ee (12) 


17. In this expression the integration has been performed 
between the limits 0 and @; or one may say that the arbitrary 
| dé 
dx 
—which it is evident they do in an infinitely long rod, from 
physical considerations. This is the object of using a long 
rod. The experiment would be easier to carry out with a short 
rod or aring heated at one end and cooled at the other; and the 
differential equation (1) would apply equally well; but in this 


constant has been chosen so as to make — and @ vanish together 


case a would have a finite value when 6=0, the right-hand 
side of (12) would not contain @ as a factor, and the whole 


calculation would become more complicated. 


Statical Curve of Temperature in a Vacuum. 


18. Equation (12) consists of two parts—the R part rela- 
ting to radiation, the S part to convection: in a vacuum § is 
zero. In order to do any more with the equation, I must take 
the two parts separately. The radiation part is the simpler. 
So let us suppose the rod on which the curve of temperature 
is being observed has a blackened surface, and is in a perfectly 
exhausted enclosure. The convection part I have only slightly 
attacked at present, and have not succeeded in doing any thing 
practical with it. Jam unable to integrate even the radiation 
part of (12) any further as it stands; so at this stage we will 
introduce our very approximate expansion (7’) for a@7—1; and 


le ek i Sb en 


fae b2 ie ti 


Conductivity of Metals with Temperature. 253 
we get the radiation part of in the form 
of ACh ey \ ( cha :) 
a) =Re{1+5 a9 + 261 +7) m+é6 
—Ré (m— 25. ape RO”, 
where a means log a, and where y is written for the correc- 


1 3) : Rc eee 
tion. factor 3% 0 1000" And this equation simplifies to 


ey = RP} ee £ (2+ma+y(ma—1)) + Fata} 


Although, - the equation looked as though it would 
contain, when put into the ordinary form for integration, a 
quartic expression under the root, and therefore would land 
us in elliptic functions, yet on working it out we find that @ 
is a factor of the expression ; and hence, the expression under 
the root being only of the second degree, the integration can 
be performed without difficulty. Integrating between the 
limits 0 and w, and between © and @, and remembering that 


aa is essentially negative, we get as the result, 


D> 


ae 2+ ma +y(ma—1) 
| sinh7! 


Fr 6m | 


_%12ma(l+y)— {2+ma+y(ma—1)\? je 


or 
L : L Maa 
sinh"(3 +5) = simh( +3) =p an) Ring 2 ae. (15) 


where L and J are used as abbreviations for certain evident 
expressions such that the ratio of J to L, which is all we need 
trouble about, is 


J 2—y+ma(1+y) 
is Rie ye a = nN Say. e ° e (16) 


It is quite possible, however, for L and J to be both imaginary, 
which happens when the second term under the root on the left- 
hand side of (14) is greater than the first. When this is the case 
I suppose the sinh becomes cosh, passing into it through infinity ; 
but the ratio J: L, or A, is always real and positive. 

Referrring back to § 7 and to equation (9), we see that a likely 
value of m for iron is 300, and for copper 650; so that for these 
two metals the value of ma is about 2°3 and 4:9 respectively. 
Looking at the expression under the square root on the left-hand 
side of (14), and neglecting squares of the small quantity y, one 


=2V Rina, . 


(13) 


(14) 


254 Dr. O. J. Lodge on the Variation of the Thermal 


sees that ma may vary between 4+5y +2 /3(1+42y) without the 
change from sinh to cosh taking place; hence the above form is 
likely to cover the case of all ordinary metals. 


19. We will denote the constant 2 a by the letter K, and 


the constant »/ Rm« by the letter », and will then write the 
equation (15) in the form 

L 7 ee 

ry +J=K cosh pet+/K?+I1sinhue; . . (17) 


or, what is equivalent, 


iF 2 auf. ee Es ee 

GB tT H4(/ 414+ Ke —3(/+1—-K)e. (18) 
/3m 

V1+5y 


its approximate value when ma=4+5y); and as m is a number 
likely to be bigger than ©, and as J is always positive and mostly 


20. Now the minimum possible value of L is (this being 


greater than 1, it follows that K, or - +J,is seldom small; and a 


reasonable value for it is about 5; hence K and ¥1+4 K? are ordi- 
narily not very unequal. For a case when they may be regarded 
as practically equal the second term of equation (18) vanishes; and 
it may be written, on this assumption, 


2 +3 2 Ko, 4. 3 Se ker 


or, putting in the value of K, namely = +J, and writing 2 = A (see 


equation 16), 


et 
an 2 cb eS e « s e 20 
: 1+ A0(1 —e-#*) wits 


Amount of Divergence of the corrected Curve from the Loga- 
rithmic Form. 


21. As the result, then, of the whole investigation, we have 
the two equivalent equations (17)‘and (18), and the approxi- 
mately equivalent equation (20); which last, however, is only 
true when K is so large that there is no perceptible difference 
between K?and 1+ K*. Itremains to see how farthese equa- 
tions agree with the results of the experiments made hitherto, 
and to show how the conductivity & and the variation-coefii- 
cient of conductivity m can be deduced from them. 

Now equation (20) obviously reduces to the ordinary loga- 
rithmic curve, which was supposed by Biot to represent the 
curye of temperature along the rod, by makingAX=0. Hqua- 


ene EY | lasaaiaiss “Une ennsibisiaia 


Conductivity of Metals with Temperature. 255 


tion (14) also reduces to the same curved = @e-“*, if we make 
m infinite and « and y both zero, i. e. if we neglect variations 
in conductivity and radiation-power ; for the numerator is 


then = 


finite. 

My brother, Mr. Alfred Lodge, of St. John’s College, Ox- 
ford (to whom I am indebted for several suggestions) has 
drawn for me the curve represented by equation (20) for some 
arbitrary and rather extreme values of the constants, viz. 


, and the denominator is indeterminate indeed, but 


1 1 5 
A= —, Say = 300 ©=3800, and p= 30: that is, the curve 
a 3007 
2—e 80 


and it is represented in Plate X., where, for comparison, is 
drawn also the logarithmic curve 


9 = 30067 a0, 


and also (by simply diminishing all the abscissze in the ratio 
3: 2) the logarithmic curve which fits the correct curve best, 
and which would have been assumed to be the correct one 
from calculation of u from observed values of the temperature 
by the ordinary formula, namely the curve 


et ae 


The value of yw is therefore not obtained correctly, at least as 
regards its absolute value, by the old process ; and the nature 
of the divergence between the new and the old curves is ap- 
parent in the Plate. 


The Method of Calculating the Conductivity and its Variation- 
coefficient by means of Equation (17) to the Curve of Tempe- 


rature, 
22. The conductivity bs is involved in the constant #4; so 


thatif one knows u, the absolute conductivity can be calculated. 
For the meaning of w refer to equations (17), (15), (11), 
(10), (9), (6), and (7), which show that it may be written in 
the following equivalent ways: 


ey) 2 DOPE toe oe € 
be =Rma= z Pa loga= B . Pa” log a= mheaer: (21) 


256 Dr. O. J. Lodge on the Variation of the Thermal 


Hence ym is inversely proportional to the square root of the 
conductivity ; and if the values of » are known for any two 
metals coated with the same varnish and otherwise under 
precisely similar conditions, their thermometric conductivities 
at zero Centigrade are inversely as yu’; so that 

12 


hig _ Po, ; 
Eo a (22) 
Or, again, the conductivity of any one metal may be ex- 
pressed in absolute measure as soon as we know yp and have 
determined the radiation-constant P (or C) by direct experi- 


ment on the rate of cooling of the rod in vacuo; for 


cow be loga | 
So Soe 
©o Po pe i 
The mode of calculating P is given in § 27 and equation (32). 
On the other hand, the variation-coefficient m is involved in 
the constant X; so that, if one knows A, it can be easily caleu- 
lated. For the meaning of 2d, refer to equations (16), (13), 
and (7), which show that its value is 
el lesa © ~); 
A= ga tet apne 5) 
or, expressing min terms of A, 
Shel ieee Vinee 2000—© 
m= og ay  B000A=76— DOTS ee! 
and as soon as m is known, the law of variation of conducti- 
vity with temperature can be expressed by the equation 
Pins ok eres 
bo AAO TH “1 Se (9) 
where b=m+274—v, ; compare equations (9) and (4). 
Hence what we have to do is to determine the constants 
and w from observed values of the temperature down the rod, 
on the hypothesis that this curve of temperature is correctly 
represented by equation (18). 


Calculation of the Constants ® and pm. 


23. Let the excess of temperature of the rod over the en- 
closure be observed very accurately (by thermoelectric or other 
means) at equal intervals all along the rod, say at successive 
distances from the origin &, 2&, 8&, &. Call any three con- 
secutive values of these temperatures 6,, @,, and 3; then it is 
easy to show from equation (18) that the quotient 


(G+I+z +3)+(F +3) 


i 


Conductivity of Metals with Temperature. 257 


is constant all down the rod, and equal to e+ e-*, or that 


eee 
—_—§$— =const* =2r say, . . (25) 


and that the value of the constant r is 
= COS eM a a.» ee, arte SED 


Hence to find w we must know 7, and to find » we must 
know 2X. | 

24. Now the only way to determine A accurately is by a 
system of trial and error, choosing it so that the expression 
(25) shall be as constant as possible all down the rod; but a 
good approximation to its value can be obtained thus. Let 
0,, 0, 0; be three equidistant temperatures near the hot end of 
the rod, and 9%, 0;, 0, three equidistant temperatures near the 
cool end ; then of course 


£ I 1 1 
ioe a ae nee 
PB a. +™ 


and therefore ; 

J iN 1 Si a | £ 
(a+ a)a—ala,* a) 
Beste ot 
Gar Oe Og. 0 BOs" 0, 


an expression which is rather long, but with the aid of a table 
of reciprocals can be evaluated without difficulty. The value 
of X so obtained may be introduced into (25) and improved 


(27) 


by successive approximations ; after which it is to be intro- . 


duced into (24) and the number m obtained, which, when in- 
serted in equation (9), expresses the rate of variation of 
conductivity with temperature for the metal experimented 
upon. ? 
é Calculation of the Constant mp. 

25. The above process, however, not only determines A, but 
also gives us a number of values for 7; and from the mean of 
these we must proceed to obtain p. 


* This equation becomes identical with the one hitherto used, viz. 
6,+4, 


=2cosh né, as soon as one puts A=0, and assumes 6, to be a geo- 


metric mean between 6, and 6,. 


Phil. Mag. 8. 5. Vol. 7. No. 48. April 1879. x 


a 


-_ i eee 


258 Dr. O. J. Lodge on the Variation of the Thermal 
To find « from (26), we may either write it thus, 
pE= cosh r= log, (rt/r—1), . . (26/) 
or, what is usually simpler in practice, we may notice that for 
the majority of metals r is buta fraction over unity, and hence 
that the number “&, whose hyperbolic cosine is equal to 7, 


must itself be very small, and high powers in its expansion may 
be neglected with impunity. Writing (26) therefore thus, 


2 cetiud aie ae 

| r= cosh wE=1+ 9 tos Sateen 
the last term written is nearly always utterly ia and 
the last but one is usually exceedingly small. Hence a first 
approximation to pm is 


pre & 2(r—1); «> co See 
and a second and generally sufficient approximation is 
pweE? 2: 9/34 6r—38)3 . . . (29) 


and as &, the distance between successive thermometers, is 
known, m is determined. 


Hapression for the Relative Conductivities of two Metals in 
terms of the Constant r. 


26. Equation (22), for the relative conductivities of two 
metals under precisely similar circumstances, becomes, there- 
fore, if the intervals & are the same for both, 


fy — CoP log (a +4/7?—1) at 
Ky yp" sey | ee tv) log log (r7+./7—1) —1) 0) 


or, to an approximation sufficient for all but very badly con- 
ducting metals like bismuth, 


Ko on. “0 Po Mv (8+6r')— —3 , & Po eel a G50) 
Ky ep" (8+ 6r) — 31 eit) GE me 
where it will be remembered that c) and pp mean respectively 
the specific heat and the density of the metal at zero Centi- 
rade. 
To determine the absolute conductivity, we must determine 


the constant P by direct experiments on cooling (see equa- 
tion 23). 


On the Determination of the Radiation-Constant P. 


27. The red, or a bit of the rod, is to be heated, as a whole, 
to some moderately high temperature, and then placed in the 
exhausted receiver under precisely the same external condi- 
tions as 1t 1s exposed to during the conduction experiments, its 


pe S ASG 


I li iii il Ni i — 


ee 


Conductivity of Metals with Temperature. 259 


two ends being rendered as impervious to heat as possible by 
means of a thickness of felt. Observations of its excess of 
temperature are then to be taken at successive intervals of 
time. If the excess of temperature 0, corresponds to the era 
of reckoning time, and if the temperature 0 be the excess after 
a lapse of time 7, it follows, since 


BaP p6(oP~ ¥) 
dt 


(see equation (5) and § 3), that 
a 


af 0 
log aS log i aa Py Pat log a; 


whence we obtain the constant required, 


im 1 1—a~—% 
‘Pa == 2 Le amper 
me logyo a 1 ed a % 


logio 5 a we \ ms fla (32) 


The Absence of Experimental Results suitable for applying the 


method of calculation to at present. 


28. To obtain experimental results suitable for applying 
equation (25), one would have to observe temperatures very 
accurately, over a considerable range of temperature, on a rod 
m vacuo with a highly radiating surface. Principal Forbes’s 
experiments were all made in air; and, as he shows, convection 
had a greater cooling effect than radiation, even on his paper- 
covered rod. The only experiments which, so far as I know, 
have been made in a vacuum, are those of Wiedemann and 
Franz ; but the range of temperature observed by them only 
went as high as 60° C. Moreover the surface of their rods 
was silvered, and the loss of heat therefore so small that they 
themselves did not regard these experiments as at all so satis- 
factory as those which they made in air. 

Moreover the rods used were not very long, and their cool 
ends were connected up with the enclosure, which would 
doubtless make =O at that end, but it would not secure 


that = should vanish at the same time: and this was of no 


consequence in their method of calculation; but it is in ours 
(see § 17). 

Again, the temperatures, though very carefully observed, 
cannot, I imagine, be regarded as accurate even to the first 
decimal place. I have Lig equation (27) to their numbers 

2 


260 Variation of Thermal Conductivity of Metals. 


for iron, after reducing their galvanometer-deflections to Cen- 
tigrade degrees by means of their little interpolation table; but 


it appears impossible to get any value for A. The form given 


is very nearly 0° 


A simple modification of their method of observing tempe- 
~ ratures, devised by Professor G. C. Foster, seems, however, 
to promise very accurate results; and it was in view of being 
thus able to observe temperatures with great accuracy that I 
set to work at the preceding calculation. © 


Suggestions for future Experiment. 

29. In any experiments which may be conducted in vacuo 
there will probably be some difficulty with the radiating sur- 
face of the rods, which should be the same for all. Silvering 
has only one objection; but that is fatal—viz. that it diminishes 
the radiation-constant so much that the heat flows down the 
rod almost asif it were a slab; moreover the convection effect 
of residual air cannot be neglected in comparison with the radi- 
ation with so great impunity as if the surface were lampblacked. 
A coating of Brunswick black would probably be perpetu- 
ally spoiling the vacuum. A close layer of thin paper (after 
Forbes) seems a very good method, or perhaps a close 
spiral of very thin cotton thread wound over the rod; but it 
cannot be said that the law of cooling in such cases is so well 
known as it is for a metallic or blackened surface. Probably 
a coating of stove-blacklead would be the best. 

Any such covering would, of course, necessitate fixed ther- 
moelectric joints, say very fine wires passed into or through 
the rod at certain accurately measured and equal intervals. 
The electromotive force generated at each joint would be mea- 
sured directly by a compensation arrangement—the arbitrary 
readings so obtained being reduced to Centigrade tempera- 
tures afterwards, either by direct experimental comparison, or 
by calculation from the following formula, 

t=N—{(N—T)’—ke}?, 
where N is the neutral point of the two metals which form the 
joint (the rod itself would do for one), T is the temperature of 
the cool joint, which may be the same all the time, e the ob- 
served electromotive force on any arbitrary scale, and k a 
constant expressing the value of this scale determined once 
for all by an observation with a known value of ¢. 

The only satisfactory method of heating is by the boiling of 
some liquid or the condensing of its vapour. Water vapour 
is scarcely hot enough, even under pressure; but oil might do. 
The heat should be conducted into the yacuum by a thicker 


ee ae sa 


The Theory of Binaural Audition. 261 


copper rod connected with the experimental rod, so that obser- 
vations of temperature may be taken in the hotter as well as 
in the cooler portions of the rod. 


Errata in No. 42 (March 1879). 
: 9P gq” : 
Page 207, equation after eq. (6), for Toga)? read 1Pa™ (log a)?. 


— 209, eq. (8’), for 247 read 274. 

Mr. Stocker, Physical Demonstrator in the Clarendon Laboratory, 
Oxford, has been good enough to point out to me, in addition to the above 
errata, that the value of log a is more nearly ‘0077 than ‘0076, as I have 
taken it, and that twice the reciprocal of this number, which in equation 
(7) is called 267, is more nearly equal to 260. 


XLIL. The Theory of Binaural Audition. A Contribution to 
the Theory of Sound. By ANTON STEINHAUSER. 
[Concluded from p. 197. ] 


6. HE results developed in the preceding theory, how- 

ever, may be influenced by many circumstances—as, 
for example, by the conduction of sound through the earth or 
through the body, and particularly by the effect of reflexion. 
For if, in addition to the direct rays which produce the inten- 
sity 7, in one ear and 7, in the other, there reach the ear other 
indirect rays by reflexion from the ground, or walls &c., then 
the intensities with which the sound is perceived in the two 
ears become respectively (7,;+ 1) and (72+ 2), where the in- 
crements of intensity p; and p, may evidently be to one another 
in any ratio whatever, according to the existing circumstances. 
Then from equation (2) we get 


(4 + p1) —(% + pe) 
tan SS tan 
esa Cake 


_ (4—t) + (p1— Ps) 
tan CEES (one) tan Se: \ Ss Paateen 
Consequently the angle « is another one than that indicated 
either by the real direction of the source of sound, or by the 
projection of the direction of the sound-rays upon the plane of 
best hearing. 

The angle at which we estimate according to the sensations 
the position of the source of sound (regarded no longer as ne- 
cessarily in the plane of best hearing) approaches the more 
nearly to the angle at which it is actually situated in propor- 
tion as p; and p2 are simultaneously diminished, and coincides 
with it when py=p,=0. This is almost attained in the case 
of weak sounds; for then the effects of reflexion, usually still 
weaker, are scarcely or not at all perceived. 


or 


262 Prof. A. Steinhauser on the Theory 


It is possible, for example, to conduct researches upon pure — | 


direct hearing, uncomplicated by effects of reflexion, by means 
of a watch removed to as great a distance as is convenient and 
held by some person in any place he chooses, whilst the ob- 
server attempts with closed eyes to discover its direction by 
its ticking. Moreover the direct action of the sound will not 
be injuriously affected by effects due to reflexion, provided 
(i, +1): (+ po) =% ¢ 293 
for then ; 
(4, + p1) — (2 + ps) mM (41%) + (p1— pa) rinse 
(atpi)+(etp2) (ath) +(pit+p2)  a+%y’ 
and therefore, if we substitute in equation (3) the value thus 
found for 


(4) ~t,) + (p1 =p) 
(4 +%) + (pi + pe) 
we again obtain the equation 


ESD 
tan «= mee tan B, 
in which e indicates the direction in which the source of 
sound is actually situated. 


But from the proportion stated above we may deduce 


tyty + 1901 = Ute + typo, 

or 

2001 = Uo 3 
therefore the proportion holds good, 

ON ae es Ose Io 

Fence the power of estimating the direction is not affected by 
the effects of reflexion, provided the increments of intensity 
thereby occasioned in the two ears are respectively proportional 
to the intensities produced by the sound directly. 

It will now be considered in the calculations which follow 
whether effects of reflexion produced by a single plane surface 
(say, for example, a vertical wall) can in certain cases fulfil 
the conditions mentioned above—that is to say, whether a 
position of the wall can be discovered in which the increments 
of intensity p, and p, arising from reflexion are respectively 
proportional to the intensities directly produced. 

As in the previous figures, let A A’ in figure 7 represent 
the line of sight, 7, and 7, the effective surfaces of the pinne, 
each including with it the angle 8, « the angle included be- 
tween the line of sight and the direction of the rays of sound 
S, which impinge upon both the reflecting wall W and the two 


Peel 


of Binaural Audition. 263 


pinne ; lastly, let the angles which the line of sight makes 
with the wall and with the reflected rays be respectively } 
and a,. 


We have, then, the following relations, amongst others, 
between these quantities :— 


a=O+y, po=a—¢d; 
a=a,+Iap=u,+2a—2¢, 


also 


and 
a= 2h — a. 
And, according to what has preceded, the ratio between the 


intensities produced by the direct action of the rays of sound 
when they make an angle @ with the line of sight is 


iy: =m: n=(tane+ tan B): (tan @—tane). 
Hence, further, it follows that by analogy the ratio between 
the intensities produced indirectly by reflexion, when the 
reflected rays of sound make the angle «, with the line of sight, 
must be | 

Pi: Po= (tana,+ tan 8) : (tan @—tanz,), 

Pi: Po=([tan (26—«)— tan B] : [tan B—tan(2¢—2a)]. 
That these ratios shall be equal requires that p,: pp=%, : to, 
or that 

[tan (2¢—«a) + tan 8]: [tan B— tan (26—2a) | 
=(tana+ tan 8): (tan 8— tana), 


2tan 8: 2tan(2¢6—a)=2tan #8: 2tana; 
from which it follows that 
tan (26—a) = tan 4. 

But since tan (26—a) may equal tan « either when 26—a=a 
or when 2¢6—a= 180° +a, we have two values for @, 
namely ¢=e« and 6=90°+<« respectively ; but of these the 
first alone has any meaning in the case under consideration, 
since, as we see from simple inspection of figure 7, ¢ cannot 
have a value greater than « if a reflexion is to be possible. 

Fence the estimate of direction will be unaffected by the re- 


flexion at a single vertical wall only if that wall runs parallel 
to the direction of the rays of sound. 


The direct rays reach both ears so long asa = 6. Similarly 
also the indirect rays reflected at the wall W will reach both 
ears so long ase, — 6. For, since -=a, +2, as may be seen 
from figure 7, it follows that «,<a always; and hence a, = 8 
as long ase = 8. 


or that 


264 Prof. A. Steinhauser on the Theory 
The rays reflected at the wall W will therefore reach both 


ears so long as this is the case with the direct rays. 

We have then obtained the following measures for reckon- 
ing the rays of sound which reach the left and ee pinnee 
respectively :— 


(1) for direct rays, the expressions 
fsin (a+) and fsin (6—«); 
(2) for indirect rays reflected at the wall W, 
fsin [26—24+6] and fsin[ —26+4+4+6]. 
Consequently we have, as a measure for the total number of 


rays of sound which reach the left and right pinne respectively, 
the expressions 


{/sin (a +8) +/sin [26-2 +6]} 


{ fsin (G—a)+/sin[—2¢6+e+8]}, 
provided the wall W is regarded as a completely reflecting 
surface. 

Therefore the intensities 7’; and 2’,, with which the sound is 
perceived in the left and right ears respectively in virtue of 
the united direct and indirect actions, will be to one another 
in the ratio of the two expressions just determined, and give 
the oe equations :— 


v,  fsin(a+6)+/sin [2¢6—2e+4+6] 


i, sin (@—a)+/sin[—26+a+ 6] 
_ sin (a+6) + sin [26+ (B-a)], 
sin (G—a) + sin [((a+f6)—2¢]’ 


and 


whence 
ee — sin[ («+ B)—2¢ | 
v%—, _ sin(#+) — sin (B—e)+sin [26+ (B—a) | 
Wj+, sin(a+f)+ sin (8—a) + sin [26+ (6—a)] 
+ sin [(«+6)—2¢] 
_ 2cosBsina+2 cos B sin (26—a) 


~ 2sin 6 cose +2 sin B cos (26—a) 
_ cos B[sin a+ sin (2p—2) | 
~ sin B[cos a+ cos (26—2a) | 

= cotan 6 tan pd 


_ tang. 
~ tan fe) 


The direction in which, then, the source of sound is esti- 


of Binaural Audition. 265 
mated is defined by the equation : 


of Sf 
t4—1t92 
tan «’ = ——, tan 6, 
tite 


or, replacing the fraction by its value just found, 
tan a’ = tan ¢. 


And hence it must follow that «’=¢, since the second possible 
value of «’, namely 180°+¢, is inapplicable to the problem, 
as is readily seen. . 

The effect which, in binaural hearing, a completely reflecting 
vertical wall exercises upon the perception of direction consists 
in this—that the observer of the source of sound seeks it always 
in the direction of the reflecting wall, independently of the direc- 
tion in which it may be actually situated. 

For example, let the source of sound be estimated to be 
situated in the line of sight, then must «’=0 and also $=0. 
This shows that the source of sound will always be estimated 
and sought for in the line of sight if the completely reflecting 
wall runs parallel to this direction. 

Again, let the source of sound be estimated to lie on the 
other side of the line of sight to that in which it is really 
situated, and in a direction making an angle with the line of 
sight equal to that which it really incloses; then obviously 
a’ = —a and alsofd=—a. | 

Finally, let the wall W so reflect the sound that no illusion 
thereby affects the perception of the direction; then e’=« and 
g@=a, which result coincides with that already found for this 
case. 

Now imagine in figure 7 an additional second reflecting 
wall W’, vertically placed, and making with the line of sight 
the angle ¢’, and let us investigate whether this cannot be so 
placed that the power of perceiving the direction will not be 
injuriously affected by a single reflexion of the sound at each 
wall. We should find, after a rather troublesome process of 
development, that the required condition will only be fulfilled 
if 


tan (6+ ¢’) =tan 2a, 
which, in consequence of the existing circumstances, can again 
only be true if 6=d/=ea. In that case both walls are paral- 
lel to the direction of the source of sound, and hardly any re- 
flexion takes place at their surfaces. 

Therefore the perception of the direction will be unaffected by 
two vertical reflecting walls only when these run parallel to the 
direction of the rays of sound. 

The results developed in the preceding paragraph concern- 


266 Prof. A. Steinhauser on the Theory 


ing the effects of reflexion on direct binaural hearing may 
possibly not entirely coincide with the phenomena actually 
exhibited, since the very conditions assumed as fundamental 
in the argument are such as cannot in actual practice occur 
all at once. Thus the rays of sound which fall upon the sur- 
faces of the two pinnz and upon the reflecting wall were taken 
as parallel to one another. Results obtained upon this as- 
sumption are consequently only approximately correct when 
the source of sound is remote from the hearer, and when the 
surface (now not necessarily considered “large ’’) of the wall 
which reflects the rays of sound to the ears lies very near to 
the hearer, since only under these circumstances can the rays 
which strike the pinnez and also the surface of the wall be re- 
garded as at all nearly parallel. 

Lastly, the reflecting walls were assumed to be completely 
reflecting; that is to say, it was assumed that the rays falling 
collectively upon the surface of the wall were sent off in 
straight lines parallel to one another. Since this is in actual 
experiment untrue, for the rays of sound suffer a partial dif- 
fusion, as do the rays of light at an imperfectly polished sur- 
face, this circumstance implies a loss of the scattered rays, 
which may be greater or less according to the nature of the 
reflecting surface. 

7. In concluding the subject of direct binaural hearing, we 
have only to add a few words on the perception of the change of 
place of the source of sound by the sensations of sound which 
are experienced when the head is not moved. 

Let us imagine a source of sound which completes a motion 
within the region in which direct binaural hearing can occur, 
and let us inquire whether, and in what way, the nature of the 
motion can be learned from the sensation of sound. We shall, 
on consideration, easily find the answer to this question on 
referring to the theory developed in the preceding pages, as 
follows :— 

The change of place of the source of sound has two conse- 
quences :— 

(1) A change of the direction in which the rays of sound 
reach the ears, and therefore a change in the ratio between 
the intensities 7; and 7 with which the sound is perceived in 
the two ears. 

(2) A change in the total intensity (4,+ 2) with which the 
the sound is perceived. 

The latter effect may result partly from a possible change of 
the distance of the source of sound from the observer, and 
partly from the change of the direction of the rays of sound. 

Disregarding the latter circumstance—for, as will presently 


of Binaural Audition. 267 


be shown, the change in the total intensity (7,+%,) caused by 
the change in direction of the rays of sound is extremely small— 
then, by what has preceded, we may conclude from the new 
ratio between the intensities 7, and 7, what the new direction 
is in which the source of sound is situated, or, in other words, 
what the motion of the source of sound to right or left may be; 
and we may also conclude by the change of the total inten- 
sity what the change of distance is, or, in other words, what 
the motion of the source of sound backwards or forwards may 
be. J¢ follows that every change of place of a source of sound 
situated within the region of direct binaural hearing may be 
known as to tts nature by the hearing of the two ears. 

For, to recapitulate, the change of place of the source of 
sound is known in respect of right and left from the new ratio 
tg +t, and in respect of forward or backward by the new sum 
Yy + tg 

From figure 3 we see that the total number of rays of sound 
reaching both ears may be measured by the length of the 
straight line de. Now this is longest when the direction of 
the rays of sound coincides with the line of sight, indicated 
in figure 8 as 8,; but it is shortest when the rays of sound take 
the direction of the line 8, (fig. 8). Hence it follows that 
the ratio between the greatest and least of the possible values 
of the total intensity, namely J,:J,, must be equal to the 
ratio between the straight lines de and gk. But since de=bc 
and gk=bv, we have the proportion 

J, 1d, = be.by, 
or, lastly, since bu=be.cos , ° 


J,:9,= 1: cos 8. 


If we take for @ its greatest possible value, namely about 
30°, in order that the difference between the two members of 
the ratio may become a maximum, it follows that 


J,:J,=1:0°866, 
whence we infer that the change in the total intensity with which 
a sound is perceived occasioned by a change of the position of 


the source of sound (supposed always to be situated within the 
region of direct binaural hearing) is very small. 


2. The Theory of Indirect Binaural Audition. 


8. If a source of sound is situated in the region of indirect 
binaural hearing, no ray of sound can reach the surface of 
either of the pinne directly ; and the sound produced by the 
sonorous body can evoke a sensation, only as the result of 


268 . Prof. A. Steinhauser on the Theory 


reflexion, provided we neglect the possible conduction of sound 
through solid bodies. | 

Whether that operation puts us in a position to form a 
judgment concerning the direction in which the source of 
sound is situated, will be seen from what follows. 

Let A A’ in figure 9 be the line of sight, 7; and f, the effec- 
tive surfaces of the pinne for rays of sound turned by re- 
flexion at the surface W from the direction S into the direction 
s, a the angle which the rays of sound make with the line of 
sight before reflexion, and «, the angle they make after re- 
flexion.. Then it is readily seen that, since neither of the sur- 
faces of the pinne can be directly reached by the rays 8, the 
hearer will receive an impression identical with that which‘he 
would receive if the source of sound were situated in front to 
the left in the direction of the reflected rays s. Now it fol- 
lows from figure 9 that 


=a + and a=¢+y, 
and that 
a=d—y, and y=a—¢. 
Substituting for y its value in the equation a*=d—y, we 


have 
a,=p—a+ d; 


a= 2p—e. 


That which is heard, therefore, indirectly in the direction a 
makes the same impression as that heard directly in the direc- 
tion e.; in which case e,, whose value is dependent on ¢, may 
without any change of the direction of the rays of sound 8, 
assume an indefinite number of different values, since the po- 
sition of the reflecting surface may as well be any other than 
it is, or there may be many reflecting surfaces. 

And since, for all remaining directions of rays of sound, the 
effect upon the ear may be radically different according to the 
nature of the surrounding reflecting surfaces, no conclusion can 
be drawn from this effect as to the direction in which the source 
of sound is situated: indeed it raises very illusory suggestions; 
for we suppose the source of sound to be in a particular direction 
in front in the region of direct binaural hearing, whereas i is 
situated behind in the region of indirect hearing. 

These illusions of the source of sound being apparently 
situated behind instead of before, do not appear always, nor 
even very frequently, and may seem quite different in different 
cases, as is proved both by the sensations which at almost every 
moment impress themselves upon the attentive observer and 


or 


roe wy ae = a" ay 
5 et = 


{ } * 


ee 


of Binaural Audition. 269 


by experiments which may be very readily made with respect 
to this point. 

The cause of this, however, lies in the particular circum- 
stances which unconsciously influence the estimate of the di- 
rection. The most important of these circumstances are :— 

(1) Trains of thought suggesting a certain direction as 
being that in which a source of sound is constantly situated. 

To give one single example :—Suppose while walking along 
a road a person hears himself called by name, he will most 
naturally conjecture that the person calling is behind him; and 
conjectures thus, not only for the reason that he does not see 
the speaker in front of him, but also specially because the very 
purpose of so calling is usually to bring to a standstill the 
person called, so that he may be more easily overtaken. 

(2) A certain indistinctness which generally characterizes 
the indirect perceptions of sound. This arises from the cir- 
cumstance that the indirect-sensations of sound are nothing 
less than a whole series of echoes following one another, and 
more or less running into one another, producing a lengthen- 
ing-out of every single element of sound, so that the last 
echoes of one element of a sound may coincide with the first 
echoes of the element immediately following it. 

Thus, for example, in hearing sounds which come from 
behind upon an open plain, as in figure 10, the sound of the 
voice of the speaker S (the arrows indicate the line of sight) 
can only reach the hearer H by reflexion at the surface of the 
earth, which is never perfectly level. Hence a sound of in- 
finitely short duration proceeding from 8 will be drawn out 
to a considerable length, since the rays of sound reflected from 
the more distant points of the earth’s surface do not arrive 
simultaneously but reach the hearer in rapid succession. 

Now it may happen that either, as is the case when the 
earth has an equably rough surface, the later echoes are weaker, 
or, as when there are reflecting surfaces, such as hills or houses 
present, the later echoes are stronger than those which precede 
them. 7 

The total impression of an indirectly perceived momentary 
sound, such as a crack, will in the former case be a dying out 
or ceasing to sound, in the latter case an irregular decreasing 
and swelling again with a rolling effect. 

This last phenomenon is perceived when thunder is heard, in 
which all the sudden claps occurring during the progress of a 
prolonged pealimply each a reflecting surface such as a moun- 
tain, causing great volumes of sound simultaneously reflected 
to arrive at certain irregular intervals. Similar phenomena 
occur also after the firing of a cannon in a mountainous neigh- 


bourhood. 


270 Prof. A. Steinhauser on the Theory 


From what has been said, it might readily be imagined that 
a direct perception of sound can be discriminated from an in- 
direct one more readily in the cases where the sound produced 
by the sonorous body is a familiar one. 

Thus, for example, by the action of an echo, the familiar 
voice of a friend, or the familiar roll of a waggon, with the 
regular tramp of its horses, will suffer a certain indefinable 
change scarcely consciously perceived, from which we shall 
conclude, either from experience or conjecture, that the source 
of sound is situated in the region of indirect binaural hearing, 
and therefore behind us. 

This discrimination becomes far more difficult or even im- 
possible if the source of sound and its varying tones be un- 
familiar; for if the sound be of a uniform character, such as 
the tone of an organ-pipe, the buzzing of an insect, the various 
elements of sound which by their united combination would 
produce echoes occur at different times, and hence can exert 
no such destructive effect on the character of the sound. But 
discrimination is most difficult of all when the sound is of an 
undecided or irregular nature, in which the separate elementary 
sounds burst forth one after the other, as, for example, in 
the sound of cattle-bells. 

As there are no other circumstances of any importance be- 
sides those which have been adduced that aid in the percep- 
tion of the direction in which a source of sound is situated, 
and as these moreover afford no exact estimate of the direction, 
we conclude that in the most favourable cases we are only in the 
position to decide that the source of sound is situated in the 
region of indirect binaural hearing. 

If we would determine with any degree of exactness the 
direction in which the source of sound is situated in such a 
case, we must, as figure 11 shows, place before the ears 7, and 
jo, and parallel to them the planes f, and /,; for these planes 
would reflect the rays arriving in the direction 8 so as to pro- 
duce an impression which would coincide with that which 
would be produced by a source of sound situated in the reversed 
direction, 8. 

9. As already previously remarked, direct sensations of 
sound almost never occur without some admixture of indirect 
sensations. 

It might therefore be contended that what has been said 
about the indirect perception of sounds might also be equally 
applied to their direct perception, and that consequently the 
alleged distinction between the two series of perceptions was 
no distinction at all. This objection may be met as follows :— 

Suppose two sounds produced simultaneously at two diffe- 


of Binaural Audition. 271 


rent points, but such that their respective ‘‘timbres”’ or cha- 
racters are somewhat different. We find by experience that 
the single ear does not sum up the impressions received from 
the two sources, but that the conceptions evoked by the im- 
_ pressions received in the ears from the one source of sound are 
separate from those evoked by the corresponding impressions 
received from the other source of sound, so that the presence 
of two separate sources of sound is known right well. 

This severing of the separate perceptions of sound becomes, 
however, more difficult the more nearly the sources of sound 
resemble one another. 

But that the ear is accustomed to such an analysis of the 
sensations, and that its analyzing-power may be whetted by 
practice, is proved by the power acquired by the conductor of 
an orchestra, who simultaneously follows the sounds of every 
separate instrument. Again, imagine, as in figure 12, that 
there is but one source of sound §, but that, in consequence of 
reflexion at the wall W, indirect rays of sound also reach the 
ears. ‘Then the united effect of these direct and indirect rays 
is obviously equivalent to that which would be produced by 
two sources of sound, one situated at 8, the other at 8). 

But the ear, by greater attentiveness and practice, resolves 
these two sounds, which apparently proceed from two separate 
sources, and which reach it in quick succession, and in resolving 
them allows itself to be led to fori a perception of the direction 
by the direct effect alone, passing the indirect effect by unnoticed. 

If, on the contrary, this analysis is not achieved, by reason 
of want of attention or of practice, or in consequence of defec- 
tive knowledge as to the finer characteristics of the direct 
sound (which an echo never completely repeats, and in con- 
sequence of which singular changes in the tone of the echo 
may be noticed), then acoustic illusions may occur, several 
examples of which have been already mentioned in the pre- 
ceding paragraphs. 

The ear, however, is no mere physical apparatus, but a sen- 
sitive organ of mind capable of being trained. 


3. Theory of Mixed Binaural Audition 


10. Ifa source of sound is situated in the region of mixed 
binaural hearing, then, as is known, the direct rays of sound 
ean reach only one of the two pinne, while both may be reached 
by the indirect rays. 

Accordingly let 7; be the intensity with which the direct 
rays of sound affect (say) the left ear, and p, the increment 
of that intensity due to the effect of reflexion. Let pz be the 
intensity of the sensation in the right ear, and due to the re- 


272 | Prof. A. Steinhauser on the Theory 


flexion alone. Then following the assumptions previously 
made, on summing up the indirect and direct effects, we ob- 
tain from equation (3)} : | 


tan a= nee Pe tan B ; 
“Hip ya ype 
and hence by calculation we can find the angle within the 
region of direct binaural hearing in which the source of sound 
is erroneously imagined to lie. 

The angle a becomes equal to the angle 8 when p, and pz 
become simultaneously zero, or indeed when p,=0, which 
may be stated as follows :—J/ a source of sound be situated in 
the region of mixed binaural hearing, we seek it always in front 
of us, and in the direction of a line drawn through the surface 
of the pinna on which the direct rays do not fall, provided 
either that the indirect rays are of null intensity, or that they 
reach the other pinna only. 

Again, if the indirect effects were known as such, and were 
separated from the direct effects, as occurs already in the theory 
of indirect binaural audition, a means of making an exact 
estimate of the direction of a source of sound would still be 
wanting ; but still at is possible by experience to perceive that 
the source of sound is situated in one of the two regions of mixed 
hearing, from the circumstance that only one ear is reached by 
direct rays, and the other is reached by none but indirect rays. 

It is situated, therefore, in the region of mixed hearing, 
respectively on the left and right sides, when direct rays enter 
only the left ear or only the right ear, ‘and when none but in- 
direct rays enter the left ear or the right ear respectively. 

Moreover, in the case of mixed binaural hearing, it is pos- 
sible to determine the region only, but not the direction, in 
which the source of sound is situated. , 


ConcLupInG REMARKS. 

11. In order to facilitate a survey of the more essential 
results of the foregoing theory of binaural audition, they are 
recapitulated and briefly set forth in the following paragraphs. 

The whole 360° of the region of binaural hearing divides 
itself into three portions :—in front, the region of direct hear- 
ing ; at the two sides, the regions of mixed hearing ; and at the 
back, the region of indirect hearing, 

Under favourable circumstances, and. without moving the 
head, we are, in consequence of our binaural hearing, able to 
decide from the sensations of sound in which region of hearing 
the source of sound is situated. 

And exact knowledge of the direction in which the source 
of sound is situated, and an estimate of any motion executed 


of Binaural Audition. 273 


by it, are only possible so long as the source of sound remains 
in the region of direct binaural hearing. 

If, on the other hand, the source of sound is situated either 
in the region of indirect or in that of mixed binaural hearing, 
we may arrive at an exact knowledge of the direction in which 
it is situated by turning the head while we seek to bring the 
source of sound :— 

(1) Into the region of direct hearing, and preferably into 
the direction of best binaural hearing. 

(2) Onto the boundary of two neighbouring regions of 
hearing. Since the direction of this boundary is known to 
each individual, the direction of the source of sound when 
brought into coincidence with this direction is also known. 
This auxiliary means offers in many cases the advantage that 
it only requires a slight movement of the head. If, for ex- 
ample, the source of sound be in the region of indirect hear- 
ing, a very slight movement of the head suffices to bring it 
onto the boundary between the regions of indirect and of 
mixed hearing. 

(3) Into the known direction of best monaural hearing. 
This happens when in doubtful cases we wish to decide 
whether the source of sound is situated in front or behind. 
For if we turn the head about a vertical axis, according as the 
source of sound is situated before or behind, the intensity of 
the sound will increase in the ear that is turned forward or 
backward respectively, since by the movement of the head the 
source of sound is brought more nearly or even quite into the 
direction of best hearing for one of the two ears. 

As may also be deduced from the preceding theory, the 
angle 8 which the surfaces of the pinne make with the line of 
sight, may, in certain circumstances, exercise no inconsiderable 
influence upon binaural hearing. Since this angle is not 
always alike in different individuals, but may differ within 
certain tolerably wide limits, the consequences which the large- 
ness or smallness of that angle may involve, are here summa- 
rily enumerated. 

For, in accordance with the preceding theory, the larger 
the angle 8 is, ) 

(1) the wider will be the region of direct binaural hearing, 

(2) the smaller will be the region of mixed binaural hearing, 

(3) the better and more distinct will hearing be in the line 
of sight, 

(4) the larger will be the region of indirect binaural hearing, 

(5) the less certain will be the estimation of direction in the 
region of direct binaural hearing, and, lastly, 

(6) the greater will be the possible difference in the total 


Phil. Mag. 8.5. Vol. 7. No. 48. April 1879. ¥ 


274 Mr. N. D. C. Hodges on a 


intensity with which a sound is perceived for the various 
positions of the head. 

The circumstances adduced in the first three points may be 
regarded as the advantages, those in the last three as the dis- 
advantages entailed by relatively increasing the value of the 
angle B. 

12. In conclusion let us finally draw attention to the fact 
that estimates of direction may be made in many cases in 
which, according to the preceding theory, the faculty of so 
doing is strictly wanting to the organs of hearing. Without 
entering further upon the circumstances involved by this ap- 
parent difficulty, be it simply remarked that often the most 
inconsiderable and apparently unimportant things are accus- 
tomed to suggest a particular position as that of the spot in 
which the source of sound is situated, so that then this power 
of finding the direction is falsely ascribed to the ear. 

Just in this manner, as estimations of depth or distance 
can theoretically be made by one eye in a very defective way 
only, and yet are again and again easily made owing to mani- 
fold circumstances which stand in no direct connexion what- 
ever with the faculty of adjustment of the eye, so also estima- 
tions of direction of sounds are made by the aid of other cir- 
cumstances without recourse to the particular faculties of the 
ear. 

Moreover, the more excitable the imagination of man is, 
the more easily will he see and hear things at a place where 
really there is nothing to see and nothing to hear. 


XLII. On a new Absolute Galvanometer. By N. D. OC. 
HopagEs, Assistant in the Physical Laboratory of Harvard 
College, Cambridge, Mass.* 


EE the ordinary form of galvanometer the current is mea- 
-2. sured by the ratio of the force it exerts on the needle to 
the directive force of the earth, the ratio being determined by 
a measurement of the angle of deflection. 

The moment of the force with which a unit current acts on 
the needle may be expressed in a series of the form 


Gigi sin 0 + Gog, sin 0Q’.(@) + &. (Maxwell, § 109). 


G,, Gz are constants depending on the dimensions of the coil, 
and 93, g2 on those of the suspended apparatus, coil or mag- 
net, as the case may be. Q’,(@), Q’;(@) are quantities which 
may vary with the deflections. 

Only in case all the terms after the first may be neglected 


* Communicated by the Author, 


new Absolute Galvanometer. 275 


are the values of the current proportional to the tangent of 
the deflection. With a single coil this is not the case. By 
increasing the number of coils and suitably placing them, the 
magnetic field may be rendered more uniform. 

In reading the deflection, either a divided circle or a tele- 
scope and scale are used. With the divided circle the deflec- 
tion may be as great as 45’, but not more, or else the instru- 
ment would not be sensitive to changes in the current. The 
use of telescope and scale necessitates much smaller deflec- 
tions. To regulate the strength of the current, shunts of small 
resistance often have to be used, and render the proportion of 
the current through the instrument doubtful. 

If, instead of placing the plane of the coils parallel with the 
magnetic meridian,| they are placed perpendicular to it, the 
sum of the force of the current and of the directive force of 
the earth would influence the magnet. 

The formula 

ie K 


me == MIG +0) ee eee ey mee (1) 
expresses the relation between the time of oscillation of a 
magnet, its magnetic moment M, its moment of inertia K, 
and the horizontal component of the earth’s magnetic force T. 

Ifthe current is passing, the following formula will hold: 

ae K 

ma Merde: 6 @ 
F being the force due to the current. From (1) and (2), 

foes (3) 

8 — i 8 e ° ° 2 e e s 


The moment of the force F on the magnet is 
C(Gin sin 0 + Gogo sin EQ’s(0) + &e.) ° 


@ is the angle between the axis of the coil and of the magnet ; 
and C is the strength of current. From this 


C(Gy91 + Go92Q/0(0) + &e.) =F. 


For the small angles through which the magnet need vi- 
brate, the second factor of the first term may be considered 
constant, and equals the constant of the instrument used as a 
tangent-galvanometer when the deflection is supposed equal 
to 90°. Let 

Gy 91 + Go92Q/o(0°) + Ke. = Koo, 


G1 + GeG192Q/2(8) + Ga. = K,, 
pS 


and 


276 Mr. N. D. C. Hodges on a new Absolute Galvanometer. 


where 


p=90°—8. 
Then 


id = CK go>. 


Substituting this value of F in (3), we get the expression 
for C, 
t?— 2 T 
C= —+ 2c eae 
ar eqgee eee =e (4) 


] 


To find the value of Ko ec, any of the ordinary experimental 
methods may be used; or, if the constant for any value of 
is known, when the same coil and magnet are used as a tan- 
gent-galvanometer, it might be obtained as follows :—Having 
a constant current, get its value in terms of Kg and the tan- 


gent of the deflection, and then in terms of the quantities in 
formula (4). 


cae. tan ¢ ; 
‘y 
v—tt T 
tt Kooe 
estes cite Ko 


It is evident that the relative values of Kg for the different 
values of the deflection of a tangent-galvanometer may be 


found by a repeated application of this process by the use of 
currents of different strengths. 


Bi 40 

gOvesdome: 
2 tang,’ 

Ke ig gamelan 


vis Tse. E “2298 moe 
Xo, tangy @  P—# 


Physical Laboratory, Harvard College, 
Cambridge, U.S. A., March 1, 1879. 


ea 


XLIV. A new Determination of the Ratio of the Electro- 
magnetic to the Electrostatic Unit of Electric Quantity. By 
W. H. Ayrton and JoHN Pzrry”*. 


[Plate XI. ] 


Introduction. 


HE fact that metals had a different power of conducting 
electricity was discovered by Sir Humphry Davy in 
1821 f, although the idea of resistance as a property of a con- 
ductor was not introduced until the publication of Ohm’s law in 
1827, in which a resistance was first regarded as a magnitude. 
Now a magnitude necessarily implies a unit of measurement ; 
but the earlier writers merely contented themselves with re- 
ducing by calculation the resistance of all parts of a hetero- 
geneous circuit into a given length of some given part of that 
circuit; so that they generally spoke of the resistance “as the 
reduced length of the conductor.” 

The next step was naturally to refer these “reduced lengths” 
to the length of some standard wire which might perhaps not 
be employed in the circuits under test, and to consider the 
resistance of unit length of this standard wire as the unit re- 
sistance. Consequently we find the unit which was employed 
by Lenz, in 1838, to be defined as that of 1 foot of No. 11 
copper wire, and the unit of Wheatstone, in 1840, as that of 1 
foot of copper wire weighing 100 grains. Until the year 
1850 measurements of resistance were confined, with few ex- 
ceptions, to the laboratory ; but about that time underground 
wires, followed shortly after by submarine cables, began to 
be employed; and when on these new lines it was no longer 
possible to determine the position of a fault by inspection, an 
intimate knowledge of the laws of electricity, combined with 
an accurate standard of resistance, became of great practical 
importance to the telegraph-engineer. The unit of length 
in the laboratory, ‘ the foot,’’ was replaced in construction by 
“the mile ;” thus the unit of resistance in England became that 
of a mile of no. 16 copper wire,and in France that of a kilometre 
of iron wire 4 millimetres in diameter. Several other units were 
from time to time proposed, of which two, that of Weber and 
that of Thomson, differed altogether from the others in their 
fundamental conception. Hxcluding the two last, all the units 
of resistance proposed were based on the obstruction offered 
to an electric current by a given length of a given material, 


* Communicated by the Authors, having been read before the Society 
of Telegraph Engineers, February 26. 

Tt “ Report to the Royal Society on the new Unit of Electrical Resist- 
ance, &c.,’” by Prof. F. Jenkin. 


278 Professors Ayrton and Perry on the Ratio of the 


-of a given section, at a given temperature ; but as'soon as it 
had been ascertained that a comparatively slight trace of certain 
impurities introduced into a conductor seriously affected its 
specific resistance, it became clear that no one of the previously 
proposed standards was sufficiently definite. Consequently 
Jacobi, in 1848, felt it necessary to send to Poggendorff and 
others a certain copper wire, since well known as “ Jacobi’s 
standard,” in order that electric copies of it might be taken, 
to avoid the growing inconvenience of the multiplicity of 
standards. 

But measurements of resistance can be conceived and carried 
out entirely without reference to the special qualities of any 
material whatever; and in 1849 Kirchhoff had effected a 
measurement of this nature : 1t was not, however, until 1851 
that Weber proposed a distinct system of measurement based 
on the fundamental units of length, mass, and time, and such 
that electrical resistance according to it would be expressed 
by an absolute velocity. Previous to this, Gauss, desiring to 
obtain precise measurements of terrestrial magnetism at 
different parts of the earth’s surface, found it necessary atthe 
outset to decide on a unit of force which was not, like the 
weight of a pound, affected by the position of the place in 
which the experiment was made. He therefore devised what 
has since become well known as Gauss’s “ absolute ”’ or relative 
unit of force, based on the fundamental units of length, mass, 
and time. In accordance with this nomenclature of Gauss, 
Weber called his method of electrical measurement the 
‘absolute electro-magnetic ’’ system. As soon as the pro- 
posed system of Weber appeared, Thomson accepted and ex- 
tended it, showing that the unit of absolute work, the con- 
necting link between all physical forces, formed part of the 
same system ; consequently the units of resistance of Weber 
and Thomson were not based on the physical properties of 
any special substance, but merely en the fundamental units of 
length, mass, and time. 

Mention must not be omitted of the mercury unit of Siemens, 
since, although not an absolute one, the coils and apparatus 
constructed by Dr. Siemens were made with such care that 
his system has materially helped in obtaining the present 
accuracy of the standards issued by the Committee of the 
British Association. 

In addition to the vagueness introduced by selecting the 
resistance of a special rod of some material as our standard, 
there would be the consequent necessary introduction of 
various numerical coefficients into the equations connecting 
current, resistance, electromotive force, work, &. Jt was 


Electromagnetic to the Electrostatic Unit of Electric Quantity. 279 


therefore though tdesirable by the Committee of the British 
Association, when appointed in 1861 to consider the question 
of the selection of electrical units, that they should decide on 
some system not only independent of any particular material, 
but also of sucha nature that every simple equation connecting 
the absolute measurements of force, work, electric and mag- 
netic quantity, current, resistance, and electromotive force 
should be independent of numerical coefficients. 

But there are, as is well known, six fundamental equations 
connecting these six quantities— 


yi fae 
I ig ? 


__ My Mg 
2. f=—z> 


oe 


one equation in fact more than is necessary to produce a single 
system of units. The consequence is that one or other of the 
two similar equations, Nos. 1 and 2, connecting electric or mag- 
netic quantity with force must be rejected. If we reject No. 2, 
then 1, 3, 4, 5, 6 determine the electrostatic units of quantity, 
current, magnetic pole, resistance, and electromotive force; and 
by rejecting No. 1, then 2, 4, 3, 5, 6 determine the electro- 
magnetic units of magnetic pole, current, quantity, resistance, 
and electromotive force. The names “ electrostatic’? and 
“electromagnetic ’’ refer of course only to the fundamental 
conception of the two systems, and do not in any way imply 
that in these systems the electricity must be in rest or 
motion: thus, for example, we may have an electrostatic unit of 
current, 


Nature of “vy,” and the importance of Measuring its Value. 


The object of the investigation described in this paper is to 
determine the value of “v,” the ratio of the electromagnetic 
to the electrostatic unit of quantity ; but 1t may be asked, since 
measurements in electromagnetic units are alone employed by 
telegraph-engineers, what interest has such an investigation 
or its results to them? The answer is, We cannot, from the 
nature of an electromotive force, have a standard cell of the 


280 Professors Ayrton and Perry on the Ratio of the 


‘same constancy as a resistance-coil*; therefore, if any one 
desires to measure with great accuracy the electromotive force 
of his battery, he is not able to do this by a simple comparison 
with a standard cell, but he must determine it absolutely him- 
self. Now the simplest way to do this, is to measure its 
electrostatic value with an absolute electrometer, and to con- 
vert the result into electromagnetic measure or into volts, by 
using the proper multiplier, which necessarily depends on the 
ratio v. 7 

There are also other practical uses that may be made of 
this constant ; but the main interest attached to the exact de- 
termination of its value consists in its constituting a test of 
the accuracy of the theory that the same medium which 
transmits the vibrations that constitute light transmits those 
also which produce electro-magnetic induction. 

For the two units of electric quantity are of a totally 
different nature from one another. If, for example, you take 
a yard and a foot, two units of length, and divide the one by 
the other, you get the simple number three, or, if you take 
two units of weight, a ton anda pound, you get a simple 
number 2240; but if you divide the electromagnetic by the 
electrostatic unit of quantity, it is more like dividing a solid 
by an area: in that case you do not get for your quotient a 
number, or a solid, or an area, buta length. So the ratio of the 
electric units is not a number but a velocity 7, and an absolute 
velocity in nature independent of the units of space and time ; 
and Prof. Clerk Maxwell has proved that this velocity must 
be that of the propagation of electromagnetic disturbances in 
a non-conducting medium, or, assuming that light is an 
electromagnetic disturbance, must be equal to the velocity of 
light f. 

1. Previous Measurements of “ y.” 


The first estimate of the relation between a quantity of 
electricity measured statically and the quantity transferred by 


* The electromotive force of Mr. Latimer Clark’s mercurous sulphate 
cell is undoubtedly very constant, but is necessarily altered by the shaking 
in travelling, by the presence, or absence, of free mercury in the paste, by 
the mode in which the mercurous sulphate paste is prepared, &c. In fact, 
as we have pointed out (Proc. Roy. Soc. No. 186, 1878), measurements of 
electromotive force are far more delicate than any chemical tests. 

t+ The dimensions of a quantity of electricity measured electrostatically 


3 , z i 1 
are eae |: measured electro-magnetically {L? M?]; therefore the di- 


L 
mensions of the ratio is Ee a velocity. (Jenkin, ‘ Hlectricity and Mag- 


netism,’ p. 164. 
{ ‘ Electricity and Magnetism,’ chapter xx. 


Electromagnetic to the Electrostatic Unit of Electric Quantity. 281 


a current in a given time was made by Faraday*; but being 
measured in arbitrary units, as the absolute system was not 
then developed, Faraday’s comparison gave no indication of 
the value of v. 

There are several ways of measuring this value. The first 
numerical determination was made, in 1856, by Messrs. Weber 
and Kohlrauscht; and their method was founded on the 
measurement of the same quantity of electricity, first in 
electrostatic and then in electromagnetic units. The result 
they obtained was 310°7 million metres per second. 

But as the quantity they measured electrostatically was prac- 
tically the amount discharged in a finite time by a Leyden jar 
previously electrified to a fixed difference of potentials, and 
the amount measured electromagnetically was the instan- 
taneous discharge of the same Leyden jar electrified to the 
same difference of potentials, 1t is probable that the result of 
the first of these measurements and consequent value of v ob- 


tained was, on account of the electric absorption of the glass, 


rather too large. 

- The next determination of the value of v was made by Sir 
W. Thomson in 1868{, who measured the same electro- 
motive force electrostatically with his absolute electrometer, 
and electromagnetically by determining with an electro- 
dynamometer the electromagnetic value of the current sent 
by this electromotive force through a known resistance. The 
mean of eleven sets of experiments, from which the highest 
value obtained was 292 and the lowest 275, gave a resuit of 
282°5 million metres per second. 

In the preceding method two forces had to be separately 
measured, one by means of an electrometer, and the other 
with an electrodynamometer ; but Prof. Clerk Maxwell, about 
the same time, carried out a method by means of which 
these two forces were made to balance one another, so that 
the ratio of the electrostatic and electromagnetic measures of 
the same electromotive force was obtained without previously 
ascertaining the value of each. The highest of the twelve 
most accurate results was 294, and the lowest 284, and the 
mean for v 288 million metres per second. In both these 
methods it was necessary to know the absolute resistance of a 
certain coil employed. 

It will be observed that even the highest values obtained 
by either Sir Wm. Thomson or Prof. C. Maxwell were lower 


* Experimental Researches, Series ili. § 362. 

+ C. Maxwell, ‘Electricity and Magnetism,’ ch. xix. p. 370. 

-{ Sixth Report of the Committee of the British Association on Elec- 
trical Standards, 1869. 


282 Professors Ayrton and Perry on the Ratio of the 


than the velocity of light, which is about 300 million metres per 
second, and their mean value far lower. 

In 1872 a redetermination of the value of v was made by 
Mr. Dugald McKichan, in Sir Wm. Thomson’s laboratory *, 
using the same method that Sir William had previously em- 
ployed ; but as certain improvements had since 1867 been 
introduced into the absolute electrometer, the results now ob- 
tained were more accurate. The mean value on this occasion 
was 293 million metres per second, still, however, being much 
lower than the velocity of light. It is important, however, to 
notice that some single values obtained were as high as 300 
million metres, although these are again balanced by others as 
low as 290 million metres per second, 


2, Method employed in this Investigation. 
Now the velocities ascertained for light are:— 


MM. Ieee hk eee Ue ee eee 
Aberration &c. and sun’s parallax 308 | million metres 

M, Foucault 2. 2 2.8 + +» » 2000 pope 

BL CGEL Ge ke oe te ee sm geet 

When, therefore, Professor Perry and myself, in 1877, took 
up the question experimentally, it could not be said that the 
ascertained value of v was equal to the velocity of light, 
although Professor Clerk Maxwell’s electromagnetic theory 
required the identity for its corroboration. 

In fact the best experiments seemed to show that v was, fer 
some reason, less than the accepted velocity of light. The 
question therefore arose, was Professor Clerk Maxwell’s theory 
incomplete, or was it that the accepted velocity of light was 
too ‘high, or was it that the methods previously employed 
for the determination of v might be improved on, and a more 
correct value obtained? This leads to the consideration of what 
other methods than those employed by MM. Weber and Kohl- 
rausch, Sir Wm. Thomson, and Professor Clerk Maxwell were 
available. Now it was possible to determine its value by an 
accurate comparison of the electrostatic capacity of a condenser 
with the electromagnetic capacity of self-induction of a coilT; 
but it seemed to us very doubtful, from the nature of the ex- 
periments, whether this method would give results more accu- 
rate than those previously obtained. And the same remark 
applied even with greater weight to the measure of a resist- 
ance electrostatically and electromagnetically, since the same 
difficulty would here have been met with that is encountered 
when it is desired to measure the insulation of a cable very 


* Philosophical Transactions of the Royal Society, 1873, p. 409. 
+t Clerk Maxwell’s ‘Electricity and Magnetism,’ p. 379. 


Electromagnetic tothe Electrostatic Unit of Electric Quantity. 283 
accurately by loss of charge. It would be possible, by dis- 


charging through a delicate tangent-galvanometer, or some form 
of absolute electrodynamometer, the charge of an air-condenser 
many times per second, to determine the electrostatic value of 
the current so produced ; and as the electrostatic value of the 
current is known from the number of discharges per second, 
from the geometrical dimensions, and the difference of poten- 
tials to which the plates are charged, we should have a fairly 
accurate means, but one hitherto unemployed for determining v. 
- But it appeared, for the following reasons, to Mr. Perry 
and myself that the method best suited for the accurate deter- 
mination of v was one that had also not been previously em- 
ployed, and which consisted in measuring the capacity of an 
air-condenser (1) electromagnetically by the swing of the 
needle of a ballistic galvanometer, and (2) electrostatically by 
the measurement of the linear dimensions of the condenser. 
A. Because the equation connecting these capacities, 


p=wK, 
k being the absolute electrostatic capacity, 
A a electromagnetic capacity, 


leads to an equation involving only the square root of a resist- 
ance ; so that if any unknown error existed in our coils only, 
the square root of that error would be introduced into the 
answer, whereas in all the methods previously employed the 
error in v was directly proportional to that in the coils. 

_B. Because only one accurate measuring instrument (a de- 
licate ballistic galvanometer) needed to be employed ; whereas 
in all other methods previously used two accurate instruments, 
such as an absolute electrometer and galvanometer, Xc., were 
necessary. 

Two difficulties, of course, presented themselves in this in- 
vestigation—difiiculties that it took us many months to over- 
come, labouring, as we were, under the disadvantage of expe- 
rimenting in a country like Japan. They were :— 

1. To obtain a large air-condenser of which the plates had 
sufficiently true surfaces that the electrostatic:capacity could 
be accurately measured—at any rate when the plates were 
not further than half a centimetre from one another. 

2. To obtain a galvanometric arrangement of sufficient sen- 
sibility to measure the small capacity of such an air-condenser, 
and sufficiently ballistic that the air-damping should be almost 
inappreciable. 

3. The Condenser. 


A BC (fig. 1) represents a vertical section of the plane upper 
brass plate 1324°96 square centimetres in area, and DE FG 


284 Professors Ayrton and Perry on the Ratio of the 


(fig. 2) the same in plan. The plate is strengthened by stout 
brass ribs D F, HG (fig. 2), and AB, BC (fig. 1). L, bl, 
are three chemically cleaned and paraffined ebonite levelling- 
screws, the ends of which are thinned to a blunt point so as to 
allow extremely little surface leakage, and by means of which. 
the plate A BC can be adjusted parallel to the lower plate, 
HJ K (fig. 1), which is shown in plan (fig. 3) ag LM N P. 
This plate is also strengthened by stout brass ribs underneath, 
LN, MP (fig. 3), and HJ. JK (fig. 2). This lower plate, 
by means of hole-slot and plane, rests on three chemically 
cleaned and paraffined ebonite levelling-screws, /,/, by means 
of which its wpper surface is made to exactly coincide with 
the top of the guard-ring QR, $% (fig. 1), and UVWX 
(fig. 3). This guard-ring is rigidly soldered to the upper 
edges of the brass box b 4, bb (figs. 1 and 3), three projections 
on the sides of which support, with hole-slot and plane, the 
levelling-screws L, L, L. Into the bottom of this box screw 
the ebonite levelling-screws /,/. Small vessels containing 
calcium chloride (not shown in the figure) are placed inside the 
brass box, bb, bb, to keep the ebonite in the neighbourhood of the 
ebonite levelling-screws /,/ quite dry, in order to avoid the possi- 
bility of surface-leakage. In the earlier experiments the space 
between the edges H K of the iower plate and of the guard-ring 
RS (fig. 1) was very small; but afterwards, to avoid the pos- 
sibility of leakage across by sparking or otherwise, this was 
increased to 2°5 millimetres, and the area of the lower plate 
thus reduced to 13823°14 square centimetres. ‘The errors 
arising from the surfaces of the condenser-plates not being 
true planes were practically eliminated by capacity-experi- 
ments being made with successive adjustments of the con- 
denser-plates, a different set of points in the upper plate being 
each time brought to the fixed distance from the lewer one. 


4. The Galvanometer. 


The galvanometer employed was one constructed some time 
back by Messrs. Elliott from our own design. It had a resist- 
ance of 19,970 ohms at 21°°9 C. In ordinary use, when fitted 
with an astatic combination, four magnets being used top and 
bottom, one Daniell’s cell would give, through a resistance of 
600 megohms, a deflection of 130 scale-divisions on a scale 
about 14 metre apart. But this arrangement, with its alumi- 
nium vane, had far too much damping for being used ballisti- 
cally. We therefore commenced by removing the vane and 
weighting the lower set of needles with pieces of brass so as 
to give it a barrel shape ; but if the brass was ight we found 
there was too much damping, and if heavy too little sensibility : 


Electromagnetic to the Electrostatic Unit of Electric Quantity. 285 


consequently all the numbers obtained for v prior to June 18, 
1878, we rejected. We now built up two little magnetic balls, 
each consisting of twenty little magnets, previously magnetized 
to saturation and slightly separated from one another with pieces 
of zinc: in each ball all the magnets pointed one way; and 
the two balls were used to form an astatic needle. As it would 
have been difficult to make the entire sphere all of magnets, 
we finished it off with segments cut from a wooden sphere. 
Now these magnetic spheres gave us an astatic arrangement 
of considerable sensibility and without very much damping, 
the decrement, or the ratio of one swing of the galvanometer- 
needle to the next, being 1:274. About June 18 we made 
experiments using this astatic combination; but fearing that 
even this decrement was too far from unity, we took the needle 
down in the interval between the 18th and 28rd, and replaced 
the segments of the wooden sphere by segments of a small 
leaden hemispherical shell, thus getting a considerable moment 
of inertia without much extra weight on the fibre. The decre- 
ment was now found to be diminished to 1:1695; and with a 
periodic time for the swing of the needle equal to 39°5 seconds 
very consistent results were obtained. 

It might at first appear that the amount of damping action 
was not very important provided it was known, seeing that 
Professor Clerk Maxwell gives, on p. 348 of his ‘ Electricity 
and Magnetism,’ the complete formula for determining the 
capacity of a condenser by the swing of a galvanometer- 
needle with any amount of damping. In reality, however, this 
formula is developed on the assumption that the resistance of 
the air is for slow velocities directly proportional to the velo- 
city ; but since we know for large velocities it is proportional 
to the square, or higher powers, and since the law is not, of 
course, discontinuous, the resistance even for low velocities 
cannot be accurately proportional to the velocity ; hence the 
only way to get perfectly correct results is to diminish the 
retardation arising from the air or other causes to nearly nil. 


5. Method of Experimenting. 


A current from 382 perfectly new porous pot Daniell’s 
cells in series was passed constantly through a resistance A B 
(fig. 4): the difference of potentials at two points, A, C, was then 
employed to send a current through the shunted galvanometer 
and through a known resistance R; and the deflection obtained 
was, say, d,. Without in any way altering the adjustment of 
the galvanometer, the connexions were then arranged as in 
fig. 5. By means of the key K, the upper plate, U, of the con- 
denser could be connected either with one pole of the battery 


286 Professors Ayrton and Perry on the Ratio of the 


or with the other. The fork I turning on the pivot P con- 
sisted of two arms perfectly insulated from one another ; the 
one 7; connected with the point A of the resistance-coils, the 
other arm /, which consisted of a piece of Atlantic-cable core 
with pointed paraffined ends (to prevent any surface leakage) 
was connected with one terminal of the galvanometer. The 
stiff wire w rigidly attached to the lower plate L of the con- 
denser and passing through a hole in the bottom of the brass 
box 6666 without touching it, could therefore, by turning the 
fork I, either (1) be connected with the pole A of the battery, 
or (2) left insulated, or (3) discharged through the galvano- 
meter. Both surfaces of contact were platinized. (The same 
set of connexions might have been arranged with an ordinary 
“charge and discharge key,” but with not such perfect ab- 
sence of leakage ; for the lever of such a key which is sup- 
ported on ebonite pillars, and along which some surface leak- 
age must have taken place, would have had to be connected 
with the wire w.) The box 06066 and the other pole of the 
galvanometer were permanently connected with A, which was 
joined to earth. 

A complete experiment was as follows :— 

1. f, pressed against w and K pressed down, so that U was 
connected with B. 

2. 7; removed from w and then K liberated, so that U was 
discharged. 

3. fo pressed against w, so that L was discharged through 
the unshunted galvanometer, producing a deflection dp. 

The rationale of the process will easily be seen. By making 
L part of the brass box while charging, we are independent of 
the action of its edge and of the shape of the curved ribs on its 
lower surface (see figs. 1 and 3); and by connecting U with 
the box before discharging L we obtain a complete discharge 
from the latter. 

The experiment was occasionally varied by leaving L insu- 
lated for some time after putting U to earth; and the apparatus 
was not considered in good order if any perceptible diminution 
from leakage was observed in the discharge of L to result from 
an insulation of several seconds. 

Let C be the current, in absolute electromagnetic units 
(gramme, centimetre, second), which flows in the first case 
through the galvanometer. 

Let a, be the angular deflection produced, 

g the resistance in absolute units of the galvanometer, 

5 2 ” ” ” shunt, 

R the resistance in absolute units introduced into the 
circuit, 


Electromagnetic to the Electrostatic Unit of Electric Quantity. 287 


G the magnetic galvanometer-constant, 
H the horizontal intensity of the uniform magnetic 
field in which the needle moyes; | 


aii v= A tan a, approximately. 


Let V be the difference of potentials maintained by the 
battery at the points A and B; then 
eee ry V 
~ stg “Th +T, —s 
s+g9 


R+ 


Mtr (stg) Rt+sg 
Let K be the capacity of the air-condenser in absolute elec- 
tromagnetic units (gramme, centimetre, second); then if a, is 
the angular swing produced by the discharge in the second 
case, and P the periodic time in seconds of the needle swinging 
freely, 
ELP 


| ee 
VK= ~G sing S A 
Bo 
ot 1 +72 (st+g)R+sg9 tana, 
Lee a s a 


a 1 +172 (stg) R+sg 2d, appro=tnaialy: 
a result quite independent of the electromotive force or resist- 
ance of the battery. 
If a is the area of the lower plate of the condenser in square 
centimetres, 
t the distance in centimetres between the plates, 
k the electrostatic capacity in absolute units (gramme, 
centimetre, second), 


A 
eet 
but 
k=v’K; 
fee) Sera nee 
iat) Ant HE Viel Ss dy 


dz is supposed to be the wndamped deflection of the galvano- 
meter ; but as there was always some slight damping even in 
our ballistic galvanometer, the following correction must be 
introduced: for d, we must write (1+42)d;, where » is the 


logarithm to the base ¢, or 2°71828, of the decrement. 


288 Electromagnetic and Electrostatic Unit of Electric Quantity. 


If now all the resistances be measured in ohms, the com- 

plete expression for v becomes Le 
ns 109172, StMR+ sg 2d, ; 

Ant P i s (1+4A).d, — 
In actual practice, of course, the mean of a large number of 
discharges of the air-condenser was employed, and great care 
had to be taken that the needle was absolutely at rest before 
each discharge—since with such a large moment of inertia an 
extremely small angular velocity meant a considerable angular 
momentum, and consequently a considerable error if disre- 
garded. Consequently, even when a number of weak auxiliary 
checking currents were employed to stop the needle while 
swinging after a discharge, considerable delay had always to 
occur between two successive discharges, while waiting for the 
needle to come to rest. 


June 18th. 
A = 1324-96 square centimetres, 
t= 1:024 centimetre, 
_— 25:3 seconds, 
— 3°0045 ohms, 
7 +r,= 8538 ohms, 
R= 12000 ,, 
8 ib 
ts+tq-~ 2000' 
= 297-34 scale-divisions, 
d= 4 20103 3 A mean of 39 discharges. 
2c= _ 0°12095. 


Weight of the magnet complete, with the forty magnets, the 
wooden segmental pieces, and the mirror, 


2°15 grammes, 
v= 297-4 million metres per second. 
June 23rd. 
A = 1323:14 square centimetres, 


t= 0:7728 centimetre, 
P= 39°5 seconds, 
a 3°0045 ohms, 
7, +7r,= 1003716 55 
R= 12000 a 
i LOrQdotess,. 
g = 19733 99 
d,= 247-75 scale-divisions, 
dual 22192 ¥ »» mean of 41 discharges, 


0:07825. 


Notices respecting New Books. 289 


Weight of the needle complete, with the forty magnets, the small 
segments cut from leaden sphere, and the mirror, 
3:4 grammes, 
v= 299-5 million metres per second. 


June 25th. 


A = 1323-14 square centimetres, 
b= 0-7728 centimetre, 
P= 42-2 seconds, 
= 3°0045 ohms, 
r, tr,= 10040 8 


R= 12000 i 
sha) al 
s+g 1000’ 
d,= 263 scale-divisions, 
Gia «UD 2D Phe! |. mean of 18 discharges, 
A= 0:081865 


Weight of the needle complete, with the forty magnets, the small 
segments cut from the leaden sphere, and the mirror, 
3-4 grammes, 
v= 297-2 million metres per second. 
Mean of the three values of v (7. ¢. the final result from the 
ninety-eight discharges of the air-condenser) is 
298 million metres per second, 
or exactly the velocity found by M. Foucault for light. 


The probable error of our answer (298) is about 1 per cent. Now 
the difference between M. Foucault’s velocity for light (298 million 
metres per second) and M. Cornu’s (300 million metres per second) 
is less than 1 per cent. We may therefore conclude that these two 
velocities for ight, as well as the value we have obtained by the 
method which theoretically ought to give the most accurate deter- 
mination for the ratio of the electromagnetic to the electrostatic unit 
of quantity, are all equal within the limits of our experiments. 


XLV. Notices respecting New Books. 


The Study of Rocks, an Elementary Text-book on Petrology. By 


Frank Ruttey, £.G.S. London: Longmans and Co. 1879. 


(THE study of rocks has of late years assumed considerable 

interest and importance. Their classification, based on their 
different origins, modes of occurrence, or mineral character, has 
been now further supplemented by an examination of the micro- 
scopic structure. 

In this latter field of inquiry the suggestive paper by Mr. Sorby* 
in 1858 led the way, which was afterwards followed by the elaborate 
researches of Zirkel and those of Rosenbusch, Vogelsang, von 
Lasaulx, Boricky, and other continental petrologists, while in our 
own country the labours of Allport, Bonney, D. Forbes, J. A. 


* «Qn the Microscopical Structure of Crystals,” Quart. Journ. G. S. xiv. 


p. 453. 
Phil. Mag. 8. 5. Vol. 7. No. 48, April 1879, Z, 


290 Notices respecting New Books. — 


Phillips, Rutley, and C. Ward have also advanced this special branch 
of geology. In fact the application of the microscope seems to be 
an essential element of petrological research, as it has afforded of 
late years more precise information concerning the mineral consti- 
tution and minute structure of rocks, than it was possible to acquire 
by the older methods of research. 

Tt is true that most manuals of geology contain descriptions and 
classifications of rocks ; but few English works have been specially 
devoted to their study. Of these Pinkerton, Macculloch, the trans- 
lations of Cotta and Jannetaz are well known; with these excep- 
tions, comparatively little has been done in this country to supply 
elementary instruction in the systematic study of rocks, although 
several good manuals have recently been published on the Continent. 
To remedy this deficiency, Mr. Rutley has prepared the above text- 
book for the guidance of students in this branch of science. 

Having specially devoted himself to this subject, and being fully 
conversant with the works of foreign and British authors, he has 
more or less plentifully interwoven original ideas and observations 
with the information derived from these sources, in the general treat- 
ment of the different subjects. 

The work is divided into two parts. The first, or rudiments of 
petrology, comprises the nature of rocks, their origin and struc- 
ture, mode of occurrence, the collecting and arrangement of them, 
the method of preparing sections of rock for microscopic investi- 
gation, followed by descriptions of the form, chemical composition, 
megascopic and microscopic characters of the chief rock-forming 
minerals, upon the identification of which the determination of the 
precise character of a rock is necessarily based. The second part, 
or descriptive petrology, contains the classification of rocks, in which 
the author to some extent deviates from that commonly adopted. 
The two principal divisions are the Eruptive and Sedimentary, 
the former being again divided into two classes—the vitreous and 
the crystalline. Besides careful descriptions of the various rocks, 
the author has prepared some suggestive and useful Tables (partly 
after the manner of Senft), showing a scheme of deviations of cer- 
tain rocks, as Granite, Trachyte, Diorite, Basalt. 

Limited to some extent as to space, which necessarily requires 
that certain portions of the subject should be treated with brevity, 
Mr. Rutley has nevertheless produced a very useful manual of 
petrology, in which the various parts are clearly and concisely 
described ; so that by a careful study of the book, assisted by the 
examination of the chief rock-forming minerals, and supplemented 
by some field-work, the student will be enabled to master this 
somewhat difficult branch of geological science. _ 


Annual Report of the Department of Mines, New South Wales, for 
the Year 1877. Ato. Pp. 212. Richards, Sydney; Triibner, 
London, 1878. 


A geological map of about 240 square miles of Upper Paleozoic 
country indicates some of the steps attained by the progress of the 
Geological Survey of New South Wales; and the many elaborate 
Reports by the relatively few Surveyors show their industry and 


Geological Society. 291 


high scientific knowledge. The immediately practical advantages 

of the science, rather than its theoretical and gradually available 

results, are mostly aimed at hy Colonial Governments, with their 
new-world notions of forcing a harvest, whether of ade minerals, 

politics, or crops, with the impatience of ‘“ ‘Teutonic gold-diggers ” 

rather than the unhurried seeking of small profits by the gradually 

enriched Chinaman. 

Hence the best geological intellects in the Colony are directly 
applied to the determination of gold-fields, the examination of coal- 
seams, and the proving of minerals, rather than to the slower map- 
ping of soils and strata, and description of the physical geography 
of the region, whether it be agricultural, pastoral, or mineral, or 
combining two or more of these characters. 

Geology, however, gives good results, in whatever direction its 
chief aim is temporarily directed ; and though hurried from mine 
to mine, the educated Surveyor observes and notes the conditions 
and structure of the country traversed, and spreads his knowledge 
as he goes. The connecting rocks between rich spots, the runs 
or leads of drifted material rich with gold, the origin of the drift, 
the le and direction of wealthy veins, and the nature of ores must 
all be studied in relation to our knowledge of similar phenomena 
elsewhere. The merely local observer and the provincial wiseacre 
are sure to lead their little world astray with crude notions, false 
conclusions, and insane crochets. Hence the policy and wisdom of 
the Colonial Government in doing the best they can to ensure their 
districts being duly geologized as far as circumstances permit. 

That an enlightened policy supports the New-South- Wales Survey 
and gets good results the present and preceding Reports fully show. 
Though taking specially a local mining aspect they are rich with 
matter that will help to advance Geology and Mineralogy, both 
practical and theoretical. 

The details of the coal-seams and their produce, and of the gold- 
works, copper-mines, opal-diggings, &c., are of especial value; and 
in view of the present scarcity of gold, to which our commercial 
depression is now said to be largely due, it is agreeable to note that 
the Government Geologist, Mr. Wilkinson, is sanguine as to new 
discoveries of Australian gold-fields. 


XLVI. Proceedings of Learned Societies. 


GEOLOGICAL SOCIETY. 
[Continued from p. 216. | 


Feb. 5, 1879.—Henry Clifton Sorby, Esq., F.R.S., President, in the 
: Chair. 
ue following communications were read :— 

1. “On the Occurrence of Pebbles with Upper-Ludlow Fossils 
in the Lower Carboniferous Conglomerates of North Wales.” By. 
Aubrey Strahan, Esq., M.A.,F.G.S., and Alfred O. Walker, Esq., F.L.S. 

The authors described the mode of occurrence near Abergele of 
certain Lower Carboniferous conglomerates, best exposed in Ffernant 


292 Geological Society: — 


Dingle, and especially of one containing numerous red- and green- 
sandstone pebbles, which enclose fossils of Upper-Ludlow forms, 
and lying above the so-called ‘“* Bastard Limestone.” From the 
arrangement of the beds the authors believe that they may have 
been deposited against a bank or sloping surface of Wenlock shale ; 
and they state that the great majority of the pebbles in the con- 
glomerate are quite unlike any rock known in the district, but 
closely resemble the Upper-Ludlow beds of Kendal and Central 
Wales. The authors discuss the origin of the pebbles, and suggest 
“the probable extension of the Ludlow beds under Lancashire as the 
most likely source from which they can have been derived.” 


2. “ On a New Group of Pre-Cambrian Rocks (the Arvonian) in 
Pembrokeshire.” By Henry Hicks, M.D., F.G.S. With an Ap- 
pendix on their Microscopic Structure, by T. Davies, Esq., F.G.S. 

In some new areas of Pre-Cambrian rocks, discovered by the 
author last summer in Pembrokeshire, some rocks of a character 
hitherto unrecognized in this country were made out. As they were 
found to hold there, and subsequently also in other areas, a very 
definite stratigraphical position, with a vertical thickness of several 
thousand feet, they have been separated by the author from the 
other Pre-Cambrian groups under the distinctive name of Arvo- 
nian. They were also found to occupy an intermediate position 
between the Dimetian and Pebidian formations, and at all points, 
so far as could be made out, appeared to be separated from each of 
those formations by stratigraphical breaks. The new areas where 
they are chiefly exposed are situated some few miles to the north 
of Haverfordwest, where they form ridges running in a direction 
from N.E. to 8.W. They occupy an average width of about a mile, 
attain at some points to a height of nearly 600 feet, and together 
have a length of over nine miles. The rocks are flanked by Pebi- 
dian and Cambrian beds along their N.W. borders; and on the S.E. 
Silurian rocks have been brought against them by faults. In general 
appearance, as well as in their more minute lithological characters, 
they are easily distinguished from any of the rocks hitherto de- 
scribed by the author as characteristic of the Dimetian and Pebidian 
groups in Pembrokeshire. They are, however, so closely allied to 
some of the true “ halleflinta” rocks of Sweden, that it seems to the 
author and Mr. Davies that this is the name that should be applied 
to them in a petrological sense. In external aspect and in their 
splintery fracture they resemble a hornstone. Under the microscope 
they are seen to consist mainly of a crypto-crystalline ground-mass, 
which, when examined with a high objective, is resolved into grains 
of quartz, with an insterstitial ingredient having but little action 
on polarized light, but which presumably is felsite. There are also 
numerous nests and fissure-like groups of quartz-grains disseminated 
throughout; and sometimes angular fragments, distinct in size and 
shape, are enclosed. These nests and fissure-like groupings are 
frequently encircled also with bands of a fibrous chalcedony, the 
structure of which is well exhibited with polarized light; and a 
rude parallelism, suggestive either of an incipient foliation or of 


On the Pre-Cambrian Rocks of Caernarvonshire. 293 


stratification, is thereby given to the rock. The author and Mr. 
Davies believe the origin of the rock to have been a sedimentary one. 

3. “On the Pre-Cambrian (Dimetian, Arvonian, and Pebidian) 
- Rocks of Caernarvonshire and Anglesey.” By Henry Hicks, M.D., 
F.G.S. With an Appendix on their Microscopic Structure, by the 
Rey. Prof. T. G. Bonney, M.A., F.R.S., F.G.S. 

In this paper the author gave the results of some further re- 
searches made in Caernarvonshire and Anglesey since his previous 
communication to the Society on Dec. 5, 1877. A brief statement 
of some of the results was read at the last meeting of the British 
Association in Dublin; but much additional evidence was now 
brought forward, besides many important facts obtained since by 
microscopical examination of the rocks. Concerning the areas de- 
scribed in his former paper much additional information was given, 
and the boundary in one case greatly extended. This new area lies 
to the west of Moel Tryfaen, and includes now, in addition to the 
central or quartz-felsite ridge, the whole of the rocks marked in the 
Survey maps as altered Cambrian, extending as far west as Glynllifen. 
Many of the large masses in South-west Caernarvonshire and the 
Llyn promontory, hitherto supposed to be intrusive rocks of Silurian 
or Post-Silurian age, were discovered, during these researches, to be 
of Pre-Cambrian age, and conclusive evidence obtained that the so- 
called altered Cambrian rocks there, and in Anglesey, were also of 
that age. In these various areas the three Pre-Cambrian forma- 
tions found in Pembrokeshire were recognized by having similar 
lithological characters, and by holding almost identical stratigra- 
phical positions in their relations to one another. Dimetian rocks 
were recognized at Twt Hill, Rhos Hirwani, near Ffestiniog, and in 
the so-called granitic ridge in Anglesey ; Arvonian rocks between 
Caernarvon and Menai Bridge, in the Eifl Range, Nevin Mountain, 
and near Ty Croes in Anglesey, &c. &c.; Pebidian rocks to the 
east of Glynllifen, Bangor, at the lower part of the Llyn promontory, 
and in many places in Anglesey. Some notes on the section near 
Ty Croes by Prof. Bonney accompanied the paper, in addition to an 
appendix by him on the microscopic examination of rock speci- 
mens from each of the areas examined. 


4. “On the Quartz-felsite and Associated Rocks at the base of 
the Cambrian Series in North-western Caernarvonshire.” By the 
Rev. Prof. T. G. Bonney, M.A., F.R.S., F.G.S. 

The great masses of quartz-felsite (or quartz-porphyry) which 
occur in the vicinity of Bangor, Caernarvon, and Llyn Padarn are 
coloured in the Survey map as intrusive, and in the memoir regarded 
as most probably the result of an extreme metamorphosis of the 
lower beds of the Cambrian series. 

The author showed that these quartz-felsites exhibited, in places, 
all the characteristics of true igneous rocks—flow-structure, fissile 
structure, and the more ordinary structure of rhyolitic rocks; that 
they were, in one place, at least, associated with masses of agglome- 
rate,and in another parted by a band of comparatively unaltered slate. 

He also showed that in several places there succeeded a grit 
formed of fragments of it, that larger fragments of perfectly 


294 Geological Soviety. 


characteristic structure, associated with others of a more slaggy and 
scoriaceous type, occurred repeatedly in the overlying beds up to 
the base of the Cambrian, described by Prof. Hughes and Dr. Hicks, 
the felsite pebbles in which come from the same source. 

Lastly, he showed that the signs of metamorphism and apparent 
“melting down” asserted to be visible on the sides of Llynn Padarn, 
proved, on microscopic examination, to be mainly superficial. 
Hence he maintained that these rocks were rhyolitic lava-flows of 
Pre-Cambrian age. 

5. **On the Metamorphic Series between Twt Hill, Caernarvon, 
and Port Dinorwic.” By the Rev. Prof. T. G. Bonney, M.A., F.B.S., 
F.G.8., and F. T. 8. Houghton, Esq., B.A. 

In the Geological-Survey map this district is coloured as “ intru- 
sive felsite,” together with those spoken of in the last paper. It 
was asserted to be probably metamorphic rock by Prof. Hughes and 
Dr. Hicks in a communication made to the Society last year; and 
the first author confirmed that view by microscopic examination of 
a specimen collected by them.- The authors had during the past 
autumn more minutely examined the district, and found :—(1) that 
the general character of the series was that of a metamorphic one ; 
(2) that the rocks of granitoid aspect were associated with well- 
marked beds of conglomerate ; (3) that this series extended up to a 
little beyond Port Dinorwic, where the quartz-felsite set in. The 
paper described the microscopic structure of some of the rocks; and 
the author expressed the opinion that the more granitoid specimens 
were probably the results of alterations of felspathic grits. 


Feb. 21.—Henry Clifton Sorby, Esq., F.R.S, President, in the Chair, 


The following communications were read :— 

1. A copy of a Letter from the late Acting Governor of the Falk- 
land Islands, relating to the overflow of a peat-bog near Port Stan- 
ley, in East Falkland. 


2. “* Note on Potkilopleuron Buckland, of Eudes Deslongchamps 
(pére), identifying it with Megalosawrus Bucklandi.” By J. W. 
Hulke, Esq., F.R.S., F.G.S. 

3. ‘“ Note on a Femur and a Humerus of a small Mammal from 
the Stonesfield Slate.” By H. G. Seeley, Esq., F.L.S., F.G.S., Pro- 
fessor of Geography in King’s College, London. 


4, «A Review of the British Carboniferous Fenestellide.” By 
G. W. Shrubsole, Esq., F.G.8. 


March 12.—Henry Clifton Sorby, Esq., F.R.S., President, in the 
Chair. 

The following communications were read :— 

1. “On Perlitic and Spherulitic Structures in the Lavas of the 
Glyder Fawr, North Wales.” By Frank Rutley, Esq., F.G.S. 

The rock, to the eye and under the microscope, has all the appear- 
ance of a felstone, but under the latter also exhibits perlitic structure 
as clearly as one of the Saxony perlites. Some of the other felstones 
of the Glyder Fawr show numerous spherulites. These felstones 
have been determined by the Survey to be lavas of Bala age. 


Intelligence and M iscellaneous Articles. 295 


2. ‘ The Gold-leads of Nova Scotia.” By Henry 8. Poole, Esq., 
M.A., F.G.S8., Government Inspector of Mines. 

The author remarked upon the peculiarity that the gold-leads 
of Nova Scotia are generally conformable with the beds in which 
they occur, whence Dr. Sterry Hunt and others have come to the 
conclusion that these auriferous quartz veins are interstratified with 
the argillaceous rocks of the district. With this view he does not 
agree. He classified the leads in these groups according to their 
relations to the containing rocks, and detailed the results of mining- 
experience in the district, as showing the leads to be true veins by 
the following characters:—1l. Irregularity of planes of contact 
between slate and quartz; 2. The crushed state of the slate on some 
foot-walls; 3. Irregularity of mineral contents; 4. The termination 
of the leads; 5. The effects of contemporary dislocations; 6. The 
influence of strings and offshoots on the richness of leads. The 
author further treated of the relative age of the leads and granite, 
and combated the view that the granites are of metamorphic origin, 
which he stated to be disproved by a study of the lines of contact. 
He also noticed the effects of glaciation on the leads, and the 
occurrence of gold in Carboniferous conglomerate. 


3. ‘On Conodonts from the Chazy and Cincinnati groups of the 
Cambro-Silurian, and from the Hamilton and Genesee-Shale divi- 
sions of the Devonian, in Canada and the United States.” By 
G. Jennings Hinde, Esq., F.G.8. 


4, “On Annelid Jaws from the Cambro-Silurian, Silurian, and 
Devonian Formations in Canada, and from the Lower Carboniferous 
in Scotland.” By G. Jennings Hinde, Esq., F.G.S. 


XLVI. Intelligence and Miscellaneous Articles. 
ON THE DIFFUSION OF LIQUIDS. BY J. STEFAN. 


[Nas memoir contains the calculation of Graham’s experiments, 
which were published in the ‘ Philosophical Transactions,’ 1861, 
p-183. To commence the experiment, on the top of 100 cub. centims. 
of a salt-solution in a cylindrical vessel 700 cub. centims. of 
water was poured. After a fixed time the liquid was, by means of 
a fine siphon, drawn off at the top in portions of 50 cub. centims. 
each, and the salt-content of each of the fourteen upper layers 
separately, the two lowermost together, determined. The amount 
of salt contained in the original solution was always 10 grams. 
The solution, corresponding to this arrangement of the experi- 
ment, of the differential equation constructed by Fourier for cal- 
culating the propagation of heat through conductors, and applied 
by Fick to the representation. of the laws of diffusion, can be 
effected in two ways :—First, in the form of periodic series. This 
form is ill-suited to the discussion of the experiments, since, except 
in a few cases, very many terms of the series must be taken for 
the calculation. . 
The second method of solution is used in the form of definite 
integrals ; and for them proper Tables are calculated. The heads 


296 Intelligence and Miscellaneous Articles. 


of these Tables contain the salt-contents of the respective layers in — 
the diffusion-vessel for a series of values of a number dependent 
on the coefficient and the duration of the diffusion. Given these 
two quantities, the corresponding distribution of the salt is found 
in the Tables. | 

Conversely, with the aid of these Tables, the value of the diffusion- 
coefficient belonging to each salt-content of a layer as given by 
Graham can be found, and we can recognize, according to the 
nature of the accordance or deviation of the coefficients resulting 
from the data of one and the same experiment, whether the experi- 
ment is in harmony with the theory or not. 

Diffusion-processes are very easily disturbed by currents pro- 
duced in the liquid by differences of temperature, so that the upper 
layers receive too much, and the deeper layers too little salt. The 
results of Graham’s experiments, however, may be more faulty still, 
and in the same direction, in consequence of those currents which 
can hardly be avoided when the liquid is drawn out with the siphon. 
We must therefore, even assuming that the theory accurately re- 
presents the processes of diffusion, be prepared to expect considerable 
differences between observation and calculation. Such differences 
occur in many cases ; but there are also cases in which the devia- 
tions are very slight. The following series give instances of the 
close approximation that may exist between observation and 
calculation :— 


TE II. III. 


Layer.| —-———~-- ~ | ——-*+ 


aS 
Cale. Obs. Cale. Obs. Cale. 


Se | pee 


} 3.984 | 3-328 | 5-392 | 5:391 | 2-936 | 3-004 


1-527 1-482 1-930 1-928 1:387 1:369 
1-317 1-290 1-282 1-287 1:236 1-225 
1-057 1:073 0°727 0-751 1-070 1:056 
0-850 0°853 0:376 0-380 0-876 0°877 
0°640 0:648 0-170 0°167 0-700 0-704 
0-460 0-469 0-071 0-064 0:542 0541 
0-318 0°325 0:024 0-021 0°:403 0°402 
10. 0-211 0-215 0-011 0-006 0:289 0°288 
Al 0:134 0°135 0:005 0:002 0204 0-199 
12. 0-081 0:082 0-003 0-001 0-135 0-133 


Bol cls BOE GS) ae 


13. 0-051 0-047 0-002 0-092 0-086 
14. 0:028 0-026 0-002 0-058 0-055 
15. 0-017 0-015 0-002 0:040 0-036 
16. 0-013 0:011 0-001 0-032 0-028 


I. refers to an experiment with chloride of sodium, lasting seven 
days, at the temperature of 9° C.; II. to an experiment with cane- 
sugar, of six days’ duration, at 9°; III. to an experiment with a 
mixture of the chlorides of potassium and sodium in equal parts, 
of seven days’ duration, and at 11—12° temperature. 

This Table shows that the mathematical treatment applied to 
the diffusion-processes gives their course with very close approxi- 
mation. 


EE 


Intelligence and Miscellaneous Articles. 297 


The motion of diffusion has two properties in common with 
wave-motion, which follow from the linear form of the differential 
equations determining the laws of these motions. The first is the 
superposition of the diffusion-currents which start from different 
parts of the liquid; the second is the complete reflection which 
the diffusion-currents undergo at the boundaries of the liquid. 
Both properties can with great advantage be made use of in the 
calculation of Tables. The memoir contains also a formula, based 
on them, which permits the diffusion-coefficient to be calculated in 
a very simple way from a combination of the salt-contents of the 
individual layers. 

As regards the amount of these coefficients k, inter alia there 
were found :— 


For Caramel (temp. 10°)...... k=0:047 
Adbmimen (GS?) oo. k=0:063 
Cane-sugar (9°).......... k=0°312 


Chloride of sodium (5°) .. k=0°765 
sf (27) ont E0016 
Hydrochloric acid (5°) .... k=1°742 
and these numbers have for base the centimetre as unit of length, 
and the day as unit of time. 

In relation to the diffusion of quantities of salt, older experi- 
ments of Graham, and Marignac’s comprehensive experiments 
especially, have taught us that the parts of the mixture essentially 
effect one another, so that the more diffusible of the two salts in 
the mixture diffuses still more quickly, and the other still more 
slowly, than when it alone is present. Also, from the experiments 
here discussed it follows, at the same time, that the distribution of 
each of the two salts, especially of the more quickly diffusing one, 
sensibly deviates from the laws of simple diffusion. So much more 
remarkable is it that the distribution of the mixture as a whole, as 
shown by the series under III., so closely conforms to those laws. 

There are two experiments of this kind specially important. 
The first refers to a mixture of chloride of potassium and sulphate 
of soda, the second to a mixture of chloride of sodium and sulphate 
of potass. Both proceed in almost the same way; and although 
Graham did not complete the analyses, it may yet be concluded 
from his statements that the upper layers contained chloride of 
potassium in the second experiment also. 

Such cases of decomposition by diffusion, as Graham calls them, 
were already known from his older experiments. Itis more correct 
to assume that the decompositions take place in the mixture before 
the diffusion, and that the latter only acts the part of a sieve which 
lets through more readily the one product than the other.— Kaiser- 
liche Akademie der Wissenschaften in Wien, math.naturw. Classe, 
1879, No. 3, pp. 24-27. 


ON THE SPECTRUM OF OXYGEN, AND ON THE ELECTRICAL LUMI- 


NOUS PHENOMENA OF RAREFIED GASES IN TUBES WITH LIQUID 
ELECTRODES. BY M. PAALZOW. 


As a rule, in the examination of the electrical luminous pheno- 


Phil. Mag. 8. 5. Vol. 7. No. 43. April 1879. 2A 


298 Intelligence and Miscellaneous Articles. 


mena of rarefied gases, the electricity is conducted to the gas en- 
closed in a glass tube through metal. wires fused into the tube. 
Since the metals are very likely to exert an influence upon the 
phenomena, I have tried the insertion of a liquid between the 
metal and the gas, in order, to some extent, to form liquid electrodes. 

A glass tube twice bent at right angles contained in its wider 
parts fused-in platinum wires and concentrated sulphuric acid, the 
latter rising one centimetre above the wires. The tube was joined 
by fusion to a mercury air-pump, the drying-vessel of which was 
filled with solid phosphoric acid. | 

The gases contained in the tube and the pump having been so 
far rarefied that an mduction-current could pass through, the 
platinum wires were connected with the poles of a Ruhmkorff in- 
ductorium, which, excited by four Bunsens, gave a striking-distance 
of 71 millims. and a deflection of 50 scale-divisions on a mirror- 
compass. (A constant current of 0°00035 Siemens-Daniell unit 
gave, on the same compass, with the same spirals, a deflection of 
100 scale-divisions. The value of the 50 scale-divisions of the 
momentary current, calculated from the duration of a vibration of 
the damped magnet and from its logarithmic decrement, amounted 
to 0:000013 8.-D. unit.) 

~The luminous phenomena observed in the tube under these cir- 
cumstances are in general similar to those seen in tubes the wires 
_ of which are provided with metal disks. 

The positive light starts from the bounding line of the surface 
of the liquid and the glass wall, and spreads, in narrower or wider 
strata (according to the strength of the pressure of the gas), to the 
vicinity of the negative liquid. 

From the surface of the negative liquid itself there rises, at some 
distance from it, a slightly conic ring of light, similarly to the flame 
of a ring-shaped burner. The intensity of this ring diminishes 
from below upwards. The more the rarefaction increases, the more 
does this negative luminous cylinder lengthen, and the greater 
becomes its distance from the surface of the liquid. With the 
strongest rarefaction the luminous phenomena are almost the same 
at both poles. The negative light makes its appearance also in the 
narrow parts of the tube*. When the entire tube is inclined so 
that the liquid surfaces are bounded by ellipses, the positive light 
emanates from the highest part of the boundary, the negative is 
most intense at the lowest point, but the entire ring of light remams 
parallel to the sides of the tube. 

The magnetic deflection of the positive and the negative light is. 
the same as that in the before-mentioned tubes with metal disks. 

The whole tube is besides filled with diffused glittering light, 
which when nitrogen is present is greenish (according to Morren 
proceeding from the formation or decomposition of the compound 
NO,+280,); without nitrogen it is bluish, and then perhaps 
arises from the vapour of sulphuric acid. This light can be msu- 
lated ; and then it gives a continuous spectrum. 

The entire luminous process is accompanied by decomposition of 

* Goldstein, Berl. Monatsber. May 1876, p. 279. 


Intelligence and Miscellaneous Articles. — 299 - 


sulphuric acid ; from all parts of the immersed platinum wires gas- 
bubbles are seen to rise. The positive wire furnishes oxygen, the 
positive liquid surface hydrogen; and it is the reverse at the 
negative side. Various other examples can be cited in proof that 
a dividing surface between a liquid and a gas may be regarded as 
an electrode. This view receives especial confirmation from the 
phenomena of occlusion*. If, namely, the current has passed 
through for a long time, one induction-shock in the same direction 
furnishes distinct gas-bubbles ; if now the current be reversed, 7-9 
induction-shocks will be necessary at the electrode charged’ with 
oxygen before the gas-bubbles are observed, while at that charged 
with hydrogen certainly 15-17 will be required. 

When the electrolytic process was continued during a whole 
week, predominantly oxygen only was obtained in the tube. Pri- 
marily, however, both oxygen and hydrogen are always separated ; 
but the latter finally precipitates sulphur from the sulphuric acid, 
which at first makes the liquid thick, and then settles to the 
bottom. 

In order to decipher and explain the complex spectrum, I was 
obliged to carry out two new operations—to produce a pure oxygen- 
spectrum, and to determine the conductivity of the pure gases 
oxygen, hydrogen, nitrogen. I permit myself here only to report 
upon the oxygen-spectrum, reserving for subsequent communica- 
tions the conductivity of the gases mentioned. 

In the tube there might be contained nitrogen, hydrogen, oxygen, 
mercury-vapour. On the spectrum of oxygen the most diverse 
results have been given by Pliicker (Pogg. Ann. evil. p. 497), 
Willner (Pogg. Ann. exxxv. p. 377), Salet (Ann. d. Chim. [4] 
~xxvin. p. 5), Vogel (Pogg. Ann. cxlvi. p. 569), Huggins (Phil. 
Trans. cliv. p. 189), Pliicker and Hittorff (Phil. Trans. clv. p. 1), 
and Schuster (Proc. Roy. Soc. xxvii. p. 383). 

The tubes for examination I filled with oxygen :—(1) after the 
method previously described, by decomposition of the concentrated 
sulphuric acid by the induction-current, when finally oxygen was 
almost solely evolved; (2) by fusing to the experiment-tube a 
voltameter containing concentrated sulphuric acid, six Bunsen cells 
being employed for the decomposition ; (3) by heating chlorate of 
potass in a retort united directly to the tube by fusion. : 

I was at length obliged to abandon the use of a gasometer and 
any other drying-apparatus than that attached to the air-pump, 
containing solid phosphoric acid, since they never furnished pure 
-results. | 

Tightening the stoppers and cocks with tallow, caoutchouc, or 
concentrated sulphuric acid gave the same results. 

The filling and exhaustion of the vessels and pump were of course 
repeated until the phenomena became constant—most frequently 
from 40 to 50 times ft. 

I have always found only one oxygen-spectrum, consisting of 

* Helmholtz, Pogg. Ann. cl. p. 483. 


t I made use of the appearance of the intensely green fluorescence-light of 
glass as a sign that the exhaustion of the tubes was as complete as possible, 


300  ~——s Intelligence and Miscellaneous Articles. 


five bright lines *. I determined their positions by means of a 
Steinheil’s apparatus with a prism, according to a scale, in which 
C De EY 255 eee. 
are situated at .... 35 | 50 | 69°5 | 74 | 87 | 117 
If the five lines from the red onwards be designated by O,, Og, O,, 


O;, O., we have 
O}, 5 Ope ston. ate 
at 45 B75 72 885 158 
With the aid of the spectral apparatus with four prisms lent me 
by M. Kirchhoff, I determined the lines according to Kirchhoff’s 
plate, according to which 
O, O; O; O. 
are situated at 935 1231 1625 2164 2489 


From comparison of these Kirchhoff’s lines with Anestrém’ s plates 
the wave-lengths of 
' Oe ets Os eee 

are 602 558°2 519 481 453 
The intensity of O, is the greatest ; then follow O, and O,, and 
last O. and O,, The lines are sharp towards the red end of the 
spectrum, fading towards the violet. Their wave-lengths agree 
best with those given by M. Vogel; only he did not observe O,, 
perhaps because the pressure of the gas was not sufficient. Plicker’s 
lines O, and O; are probably mercury-lines. 

Contrary to Mr. Schuster’s latest statement, I find the spectrum 
of pure oxygen equally at both poles. I find this identity in the 
hydrogen also, and in the nitrogen only an intensifying of two of 
its lines (95 and 125 of the first scale). If the gases are not pure, 
other lines may come in at the negative pole, because the ponder- 
able mass is thrown off at that pole. 

I have intentionally employed only simple induction-currents, 
because with the rapid and violent discharge of a Leyden jar por- 
tions of the electrodes and glass sides may be carried along in the 
discharge-current, which with the quiet discharge of the simple 
induction-current remain undisturbed in their places. At all events 
I hold that the question whether there is a plurality of spectra of 
a pure gas is still an open one, and am inclined rather to ascribe to 
each simple gas one spectrum only. With oxygen, which I have 
pursued within variations of pressure from 200 millims. to the 
most extreme rarefaction, I have never seen any other lines than 
the five named ; and these, brightest at 2 millims. pressure, dimi- 
nish in brightness in both directions from that point, so that at 
very inconsiderable and at high pressures only a glimmer of light is 
visible, which I would not call a continuous, but much rather an 
indistinct spectrum.—Monatsbericht der kiniglhch preussichen Aka- 
demie der Wissenschaften zu Berlin, Sept. & Oct. 1878, pp. 705-709. 

* Between Og and O, three, before O, four, and behind O, one broad streak 


of light are to be seen, but so faint that ie can never be confounded with the 
five lines ; besides, they are quite destitute of a sharp margin, and cannot be 
analyzed with the four-prism apparatus, 


THE 
LONDON, EDINBURGH, axp DUBLIN 
PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES.] 


MAY 1879. 


XLVIII. On the Formation of Emulsions, and the Action of 
the Bile in Digestion. By Dr. G. QUINCKE*. 


1. Historical Review. 
N emulsion consists of a large number of small spherical 
globules of fatty matter suspended in an aqueous liquid. 
Ordinary milk, for instance,isan emulsion. The smaller these 
fatty globules the larger is their surface in proportion to 
the mass, and the greater is the resistance they meet with 
in ascending through the specifically heavier surround- 
ing fluid. The smaller the fatty globules the longer they 
remain suspended in the surrounding liquid, and the more 
perfect is the emulsion, The minute globules have a con- 
tinual tendency to coalesce into larger ones; the less this 
tendency and the smaller the uniform velocity of the ascent 
of the globules in the surrounding aqueous liquid, the more 
permanent is the emulsion. And the smaller this velocity the 
less is the difference between the specific gravity of the emul- 
sion and that of an actual solution of the fatty matter in the 
liquidf. 

In chemists’ shops an emulsion is made by diffusing mecha- 
nically (rubbing with a pestle in a porcelain mortar) the glo- 
bules of an oil throughout a solution of gum arabic in water. 
In the process of digestion in the animal body the assimilation 
of the fats is initiated by the formation of an emulsion in the 
liquid contents of the intestine, and, as experience shows, faci- 

* From a separate impression from Pfliger’s Archiv fur die gesammte 


Physiologie. Translated by J. F, Iselin, M.A, 
Tt Camillo Bondy, Pogg. Ann. 1865, p. 8323; E. Mach, 70. p. 329. 


Phil. Mag. 8. 5. Vol. 7. No. 44. May 1879. 2B 


802. Dr. G. Quincke on the Formation of Emulsions, 


litated by the bile. It is, on this account, as a physiological 
question that the development and durability of emulsions has 
more especially been studied. 

W. Kiihne (Physiologische Chemie, p.129, 1866) and Briicke 
(Wien. Sitzber. 1870, Ixi. 2nd part, p. 863) were among the 
first to demonstrate the influence of the soaps developed in 
the small intestine on the formation of emulsions. The latter 
showed. that rancid oil, containing free fatty acid, when 
agitated with dilute solution of the alkaline carbonates, 
produces a perfect emulsion with much greater rapidity 
than a neutral oil. He pointed out at the same time the 
important part. played in the process of digestion by the 
free fatty acids, which, according to the discovery of Claude 
Bernard, are separated in the intestinal canal from the 
neutral fat by means of the pancreatic juice. More recently 
Johannes Gad* made the interesting observation that small 
quantities of oil, which contain free fatty acids, will form per- 
fect emulsions by mere contact with alkaline solutions without 
the aid of external or mechanical means, such as agitating or 
stirring. This can be well shown by dropping a little cod- 

liver oil into a *25-per-cent. solution of soda. 
From further investigation it appeared that the emulsifying 
power depends on the viscosity and acidity of the oil, on the 
concentration of the soda solution, and on the solubility in the 
surrounding fluid of the soap formed from the fatty acid. By 
adding common salt and bile to the alkaline liquid, this ten- 
dency to dissolve is so far corrected that the facilities for the 
production of a good emulsion are much inereased. With 
eastor-oil, which is more viscous than other oils, the formation 
of an emulsion was not observed. When the conditions for the 
emulsion-formation were present, the surface of the drop of oil 
threw off at once a milky substance into the surrounding liquid; 
the drop formed protuberances at the side, and exhibited 
alterations in form and movements which possess remark- 
able similarity to those of the Amaba. Smaller oil-globules 
then split off; and these partly gave rise to the further pro- 
duction of emulsion. Under the microscope witha low power 
the vicinity of the drop was seen to be the scene of brisk action ; 
the particles producing turbidity in the fluid were observed to 
fly off in rapid gyrations from the surface of the drop, some- 
times returning to it again. ‘The remainder of the oil could 

not by mechanical means be converted into emulsion in the 
- same liquid. | 

Gad recognizes therefore, quite correctly, the conditions 

* Du Bois-Reymond’s Archiv fiir e un ysiologie, 1878 
pp. 181-205, ymond’s Archiv fiir Anatonue und Ph ysrologre, 1 78, 


and the Action of the Bile in Digestion. 308 


for emulsion-development, not in the soap dissolved in the 
liquid, but in that which forms more or less rapidly on the 
surface of the oil, where, in fact, the fatty acids contained in 
the oil come into contact with the alkaline liquid. He then 
proceeds to observe that when the soap that has been formed 
under the given conditions is soluble in the surrounding liquid, 
it is by diffusion carried off radially from the point where it is 
developed, while inside the globule the equilibrium of solu- 
bility is maintained by diffusion of the fatty acid outwards 
towards the periphery. If the soap be so rapidly formed and 
removed that the fatty acid by diffusion towards the periphery 
cannot make up the deficiency, the outer edge of the globule 
will alter its shape, and there will be thrown off smaller fatty 
particles which are not enclosed in a soapy membrane. But 
when the rapidity with which the soap is formed reaches a 
certain point, the latter will not be dissolved by the surround- 
ing liquid, and the oil-globule will be enveloped by a soapy 
membrane. The development and displacement of the soapy 
matter will give rise to a change of volume in the liquid ; and 
this in its turn will cause the breaking-away of small fatty 
particles, each of which is enclosed in a film of soap. Should 
there be from any cause an irregularity in the course of the 
formation of the soapy membranes, it will occasion Ameba- 
like movements, the protuberances being extended at the points 
where the membrane takes a longer time to thicken. 

To these theoretical views, however, [ am unable to assent, 
because it appears to me to be highly improbable that mere 
diffusion currents can produce movements so energetic as those 
that are observed in the production of emulsions. In the fol- 
lowing pages I shall endeavour to prove that the formation of 
an emulsion depends essentially on the existence of thin scales 
of soap solution dispersed over the common surface of the oil 
and the liquid, and also that the so-called Ameba-like move- 
ments depend on the same cause. 


2. The Bounding Surfaces of Liquids in Contact with Aw 
and with Water. | 


The surface of every liquid, whether the same be bounded 
by air or by another liquid, has a tendency to become as 
small as possible, or, as it is commonly termed, has a certain 
tension. The magnitude of this tension, which may be likened 
to that of a cloth, or to that of the envelope of a caoutchoue 
balloon, or of an inflated pig’s bladder, is measured by the 
force (in milligrammes) exerted on a strip of the surface one 
millimetre broad. The tension of the surface of a liquid 
bounded by air is at the same time a measure of the cohesion 

2B2 


304 Dr. G. Quincke on the Formation of Emulsions, 


of the liquid, and is generally found by multiplying together 
the height at which the fluid will stand in a capillary glass 
tube, the radius of that tube, and half the specific gravity of 
the fluid. 

In consequence, however, of the difficulty of thoroughly 
moistening the interior of the tube with the fluid, this method 
is not quite accurate. It is a better way to determine the 
tension by measuring the vertical distance between the apse 
and vertex of a large flat bubble of air lying in the fluid un- 
derneath a horizontal glass plate; the square of this distance 
into half the specific gravity of the fluid gives the surface- 
tension directly, independent of the nature of the plate under 
which the bubble lies. The shape of such a bubble is the same 
as that of an inverted dewdrop in air. By forming a flat 
bubble of some other fluid in the heavier fluid (for example a 
bubble of oil in water) the surface-tension of the common 
surface of the two fluids may be found in a similar way—for 
instance, in this case by multiplying the square of the vertical 
distance between the bubble’s apse and vertex into half the 
difference of the specific gravities of oil and water. 

We find by this method the tension at the common surface 
of air and water to be = 8°25 mgr., of air and olive oil =3°76 
mer., of water and olive-oil =2°30 mgr. Other fatty oils, 
rape-oil, almond-oil, castor-oil, cod-liver oil, &c., give similar 
results. fluids which mix with water in all proportions, like 
alcohol or dilute salt solutions, form neither bubble nor glo- 
bule in water; the tension of the common surfaces of such 
fluids and water is =Of. 


d. The Dispersion of Soap Solutions and of other Fluids over 
the common Surface of Oil and Water. 


When some other fluid is applied to an air-bubble in water, 
and it disperses itself over the surface of the bubble, the ver- 
tical distance between the vertex and apse of the latter is di- 
minished ; in other words, the tension at the common surface 
of air and water has been reduced. Tor instance, when olive 
oil is dispersed over the common surface of air and water, the 
air-bubble is coated -with a thin film of oil ; and the surface- 
tension is now compounded of the tension at the surface of air 
and oil, and of the tension at the surface of oil and water. 

* Compare G. Quincke on the Cohesion of the Solutions of the Salts , 
Poggendorft’s Annalen, clx. p. 369, 1877. ; 

+ The more detailed explanation of these physical laws, as well as of 
the theory of the dispersion of one fluid substance over the surface of 
another, I have given with mathematical and experimental illustrations 


in Poggendorff’s Annalen, cxxxix. p. 1, 1870; 76. clx. pp. 887 and 560, 
1877 ; and in Wiedemann’s Annalen, ii. p. 144, 1877. 


ee ee 


ES ee = 


and the Action of the Bile in Digestion. 305 


In a similar way a fluid like soap-solution will spread itself 
over the surface of a flat oil-bubblein water. At the common 
surface of soap-solution and olive-oil the tension is =0°36 
megr.; but at the common surface of soap-solution and water 
the tension is =0;and as the original surface-tension of olive- 
oil and water is 2°3 mgr., this tension has been reduced to 
the extent of 84 per cent. by the dispersion of the solution of 
soap. . It will be found that the oil-bubble itself has been made 
considerably flatter and broader by the dispersion. 

The alteration in form of an air- or oil-bubble increases with 
the thickness of the film of the applied fluid, and attains its 
maximum value when that thickness is more than’0001 millim., 
or one-fifth of the length of a mean light-wave in air. The 
thickness of such a film therefore cannot be recognized by even 
our best microscopes; for they only detect a distance equal to 
half a wave-length*. As exceedingly dilute solutions of soap 
(1 per cent. and less) are able to produce this effect, we ob- 
serve that an excessively small quantity of solid soap, which 
in any other way we could scarcely detect, is sufficient to 
cause this phenomenon of dispersion. And this dispersion 
takes place with great rapidity; a drop of olive-oil will spread 
itself over the surface of still water in a single second, and 
cover a space several metres in diameter. 

Similar to the action of soap-solution is that of diluted 
ox-gall, or of a fluid obtained from the action of a dilute solu- 
tion of soda on the free fatty acid contained in oil. Ina rectan- 
gular glass trough a horizontal plane glass plate was suspended, 
the latter being pierced in the centre witha hole of 2 millims. 
diameter. The trough was then filled with water up to the 
lower surface of the glass plate; and through the hole, by means 
of a pipette,a globule of oil was introduced underneath the glass 
plate. With a second pipette a few drops of a *25-per-cent. 
solution of soda were introduced; and this immediately sank 
in the oil and retreated to the lowest-side of the globule. The 
soda formed with the free fatty acid a soap, which then en- 
veloped the drops of soda solution lying in the oil with a more 
or less thick whitish membrane. If this membrane be then 
broken up by agitation, or by its coming into contact with and 
dissolving in the adjacent water, the solution of soap or a mixed 
solution of soap and soda spreads itself over the surface of the 
globule of oil, and the latter becomes flatter and broader. 


* The proof of these propositions will be found in my treatise “ On the 
Distance at which the Molecular Force of Capillarity can act,” Poggen- 
dorfi’s Annalen, cxxxyii. p. 402, 1869; also “On the Hdge-angle and 
Dispersion of Fluids on Solid Bodies,’ Wiedemann’s Annalen, ii. p. 177, 
1877 (Phil. Mag. [5] vol. v. pp. 321, 415). 


306 Dr. G. Quincke on the Formation of Emulsions, 


Simultaneously with this dispersion of the soap-solution, a 
current is set up from the interior of the fluid towards the 
centre of dispersion, and continued onwards from its surface. 
This current is much stronger in the tenacious oil than in the 
water. The bubble becomes for a short time concave at its 


vertex ; isolated particles of oil are torn away by the cur-— 
rent from the main body, and form spherical globules in — 


the surrounding aqueous fluid; and vortices are produced in 
the oil similar to those caused by blowing a stream of air 
through a vertical and narrow glass tube on to a free and 
plane surface of oil. Ifa layer of oil of from 5 to 10 milli- 
_ metres thickness be poured on water, and alcohol allowed to 
spread itself over either the upper or under surface of the 
oil, those parts of the oil which are opposite to the centre of 
dispersion will move towards that centre ; the layer of oil may 
even be pierced by this means, so that air and water come into 
contact. Excessive rapidity of dispersion in the applied fluid, 
or too much tenacity in the oil, will impede the expulsion of 
the oil particles or the piercing of the oil layer just as much 
as sluggishness in the dispersion or too great ductility in the 
oil. 


4, Explanation of the Spontaneous Formation of Emulsions 
by means of Dispersion. 

By the phenomena described in the above paragraphs we 
are now able to explain the formation of an emulsion. 

When a solution of soda and an oil come into contact, a solid 
soap is formed by the action of the free fatty acid of the oil. 
Gradually a portion of this soap dissolves in the adjoining 
aqueous fluid. So soon as the fluid solution of soap comes 
into contact with the oil, it spreads itself over the bounding 
surface of the oil and aqueous fluid, and carries with it the 
undissolved particles of soap with any adhering oil-globules. 
In this way there are detached from the oil and borne into the 


adjoining fluid a number of filaments, which, possessing the ~ 


tendency to assume the shape of bodies of least surface, are 
converted into larger or smaller globules of a spherical form, 
just as a jet of water in the air breaks up into larger and smaller 
drops. To a certain extent this conversion of the oil into glo- 
bules will be retarded by the solid and fluid soap already pre- 
sent or newly formed; and then the length of the filaments 
will be increased, or the size of the nascent globules diminished. 
By the original dispersion, however, fresh oil particles will be 
brought into contact with the soda solution, and after a time 
the newly formed solid soap is again dissolved and a second 
dispersion occurs. Similar periodic dispersions of oil on the 


ee Se os ee eee 


Se 


| 


and the Action of the Bile in Digestion. - 807 


surface of still water were observed and described by me nine 
years ago (Poggendorff’s Annalen, cxxxix. p. 76,1870). 

The periodic dispersions of soap solution over the common 
surface of the oiland an aqueous fluid, which are not simulta- 
neous at all points of the oil-surface, will be found to be con- ~ 
nected with vortex-movements in the interior of both fluids, and 
to draw the oil more especially towards the dispersion-centre. 
This is the cause of the Ameba-like movements at the edge of 
the main mass, while the detached particles of oil form the emul- 
sion. In fact, under the microscope, not only the aqueous 
fluid can be seen, but also, and more conspicuously, the oil in 
the vicinity of the common surface, in a state of gyration. 

When the oil possesses a tolerable degree of toughness, and 
the dispersive force at the common surface of the two fluids is 
moderately great, the vortex-movements and the detached 
oil particles will be very numerous, and may be produced, as 
indeed follows from the dispersion theory (see above, 3, p. 805), 


- by means of films of diluted soap solution not exceeding in 


thickness a few millionths of a millimetre. A very minute 
quantity of soapy matter is therefore sufficient to produce the 
appearances in question. ‘The free fatty acid necessary for 
the formation of this soap is nearly always present in oil, and 


_ reaches the surface of the latter by means of diffusion. It can 


be produced in the fluid contents of the intestine by means of 
the pancreatic juice, and in the open air by the action of car- 
bonic acid on the neutral alkaline oleates*. If the soap be 
formed too rapidly, the common surface of the oil and the 
aqueous fiuid is coated with a film of solid soap. Hence the 
oil-surface becomes immobile, and the dispersion and its con- 
sequences are impeded or are altogether wanting—just as, in 
Leidenfrost’s experiment, when water is brought into contact 
with red-hot metal the formation of steam is impeded or does 


~ not occur at all. 


In the same way the consequences of the dispersion, the 
formation of emulsion and the movements of the particles of 
oil, will be prevented, if only a very small quantity of soap be 
formed, or if the soap be dissolved too rapidly by the surround- 
ing fluid. Hvery, even the minutest, particle of soap will 
then immediately be diffused in a solution, and the dispersive 
energy will not be sufficient to produce the vortex-movements 
in the oil, and to detach the particles of that substance. Ifa 
mill-brook be allowed to trickle in a small stream over the 
water-wheel, the latter will not be set in motion; but by perio- 
dically damming it back a small body of water can be made 
with advantage to produce mechanical work. 

* Compare Heintz, Zoochemie, p. 439. 


308 - Dr. G. Quincke on the Formation of Emulsions, 
d. Solid and Liquid Films at the common Surface of two Fluids. 


Castor-oil. 


For the reason last stated, castor-oil will not freely form an 
emulsion. 

When a drop of a fixed oil is allowed to fall at as small a 
distance as possible from the end of a glass rod onto a layer 
of a dilute solution of soda which is only a few millimetres in 
thickness, and is contained in a watch-glass of from 50 to 100 
millimetres diameter, the oil will generally, as explained more 
fully above (in 3), disperse over the surface of the liquid; for 
the surface-tension of the more perfect fluid is greater than that 
of the oil. Shortly afterwards soap is formed and dissolved in 
the aqueous liquid, the tension of the free surface of the 
aqueous liquid becomes considerably less, and the oil contracts 
again into a lenticular-shaped drop. On its lower surface the 
drop of oil is coated with a film of soap, which may consist of 
a thin membrane either of liquid solution of soap or of solid 
soap. The latter is well seen when a number of solid particles 
of soap lying close to each other form a whitish matted film, 
as in the case of cod-liver oil in a from 1} to 2-per-cent. solu- 
tion of soda. 

If the soapy membrane be liquid, the oil-drop assumes a 
spherical form, which it will retain even when the liquid in 
the watch-glass has a rocking or rolling motion communicated 
to it. If, on the other hand, the membrane be solid, the drop 
under the rocking motion takes a cylindrical shape, which dis- 
appears more or less slowly in proportion as the membrane is 
thicker or thinner. This was the case with olive, almond, 
and cod-liver oils in a 0°06-per-cent. solution of soda, and of 
almond-oil in a 0°25-per-cent. solution. A similar appearance 
is observed in the case of a drop of mercury in a clean watch- 
glass, which, when coated with a thin layer of oil, retains its 
spherical form, notwithstanding its being rolled about on the 
glass. If, however, the mercury contain a small quantity of a 
solid metal, as, for example, lead, which forms in contact with 
the air a film of solid oxide, the drop will become cylindrical 
under the influence of a rocking motion. 

With castor-oil in dilute solutions of soda, I have observed 
atter the lapse of some hours a trace of a whitish precipitate 
at the lower surface of the oil-drop; but the latter is always in 
the shape of a sphere. When shaken, the drop becomes larger 
for a few minutes, probably because the agitation causes a little 
soap to be thrown from the interior of the drop to its surface, 
where it is dispersed. But so soon as this soap is dissolved in 
the aqueous fluid, and the common surface of the two liquids 


and the Action of the Bile in Digestion. 309 


returns to its former condition, the drop of oil will also assume 
its original shape. 


6. The Influence of Bile. 


For the bile that I employed in my experiments I am in- 
debted to the kindness of my colleague W. Kiihne; it was 
prepared by evaporating to dryness over the water-bath an 
alcoholic solution of crystallized ox-gall, and dissolving the 
residue in water. 

If some solution of bile be added to the fluid in which floats 
a drop of olive, almond, or cod-liver oil coated with a solid 
soap membrane, this membrane will be dissolved ; the oil-drop 
assumes the spherical form, and retains it after agitation. On 
this ability of bile to transform a solid into a fluid soap, or into 
a soap-solution, seems to depend its property of promoting the 
assimilation of fat in the animal body. Solid particles of soap 
on the surface of an oil-drop prevent any change of form in 
that surface, and thus diminish its ability to pass through ani- 
mal membranes. This hindrance is removed so soon as the 
drop is coated with a fluid membrane. Bile has the property 
of promoting the spontaneous formation of an emulsion when 
the solid soap at the common surface of the oil and the soda- 
solution dissolves slowly ; but it counteracts the emulsion-for- 
mation when it converts the solid soap into a liquid too rapidly. 
Both of those phenomena were observed by Gad. 

According to the views of C. A. von Wistingshausen*, 
the bile, drawn through the walls of the lacteals, is accom- 
panied by the adhering particles of fatty matter; but, as it 
seems to me, this theory has not up to the present been 
proved. The same observer claims to have found that olive- 
oil will rise higher in capillary tubes moistened with various 
liquids when those liquids contain in solution salts of the 
biliary acids. For moistening the tubes, water and dilute solu- 
tion of potash were used, with or without the addition of 
albumen. 

Unfortunately we are unable to gather from the descriptions 
of these experiments in what way the capillary glass tubes were 
moistened with the liquid. Ifthe oil in rising drives before it a 
continuous layer or column of the liquid, my own experience is, 
contrary to that of von Wistingshausen, that oil will rise higher 
in capillary tubes wetted with water than in those moistened 
with solutions of bile of different degrees of concentration. In 
the presence of potash it may behave differently ; the solid soap 

* Compare J. Steiner on C. A. von Wistingshausen’s “ Researches on the 


Action of the Bile in the Absorption by Endosmose of the Neutral Fats,” 
Du Bois-Reymond’s Archiv, 1873, p. 139. 


- 


310 ~=Dr. G. Quincke on the Formation of Emulsions, 


at the common surface of the oil and aqueous liquid renders 
the fluid column in the capillary tube less mobile; and there- 
fore prevents the oil from rising so high. But by the addi- 
tion of the solution of bile the soap is rendered soluble, the 
friction in the interior of the tube is diminished, and conse- 
quently the height to which the oil rises is indireetly increased. 
_ Ithas been often stated (compare Gad, Du Bois’s Arch. 1878, 
p- 202) that from experiments of this kind we obtain an idea 
of what takes place on a very much reduced scale with the 
diffusion of fluids through the capillaries of the animal mem- 
brane. But it must be remembered that the ascending action 
in capillary tubes depends on the nature of two surfaces—one 
the common surface of water or aqueous fluid and air, the other 
that of the same substance and oil. Now the first of these, 
on account of its greater surface-tension, has a much more 
decided influence on the capillary height than the second. 
And it also happens that the height varies with the curva- 
ture of the common surface of the oil and the fluid; in glass 
tubes the convex side of the common surface is generally 
turned towards the aqueous liquid. But this curvature will 
vary considerably in the same tube, and depends materially on 
the edge-angle of the common surface with the wall of the 
tube ; and the edge-angle has very different values in the case 
of tubes of glass and of those of the animal membranes. Now, 
under normal circumstances the surfaces of the fluids of the 
animal body are in contact neither with glass nor with air ; 
consequently no opinion can be formed of the operations of 
diffusion in the animal body by the measurement of capil- 
lary heights, which depend essentially on the common surfaces 
of fluids with glass and air. A closer insight into these phe- 
nomena of diffusion can only be obtained by an investigation 
of the physical and chemical actions at the common surface 
of one kind of fluid with another, or with the animal mem- 
brane itself. 


7. Permanence of Emulsions. Froth. 


J. Plateau (Mém. de Brux. xxxvii. p. 3, 1868) first showed 
that many liquids appear to possess greater viscidity on their 
outer than on their inner surface. More recently I myself 
(Poggendorff’s Annalen, cxxxix. p. 71,1870), as well as Maran- 
goni (Cimento [2], v.—vi. p. 239, 1872), found that a free liquid 
surface in contact with the air becomes Jess mobile as soon as 
a thin film of some extraneous fluid is diffused over it. ‘The 
same thing occurs when an extraneous liquid (solution of soap) 
is diffused over the common surface of the other liquids (oil 
and water). 


ee — HSE ET — 
ee —— _ 


and the Action of the Bile in Digestion. dll 


The immobility or permanence of the common surface thus 
modified is explained by the fact that each opening in the film of 
extraneous liquid is immediately closed by the molecular forces ; 
the surface-tension of the pure liquid in the opening is greater 
than that of the rest of the film contaminated by contact with 


the extraneous liquid. The extraneous film may also consist 


of a solid body, provided that it be not completely solid, but to 
some extent mobile. This follows from the above-described 
(under 5) phenomena and properties of the common surfaces 
of liquids and solid bodies (compare Wiedemann’s Annalen, 
np. 145, Lott). 

In emulsions of the fixed oils in a solution of soda, the thin 
film of soap, each aperture in which is closed again by molecular 
force, prevents the oil-globules from coalescing. In emulsions 
of gum as prepared by the druggists, each minute oil-globule 
is separated from the aqueous fluid by a film of the solution of 
gum; for at their common surface with gum-solution the fixed 
oils have a less surface-tension than at that with water; this 
property I have proved by special measurements, as I shall have 
occasion to explain at greater length in another place. The 
longer the gum-solution remains attached to the surface of the 
oil, the firmer it will adhere. 

When mercury is agitated with water and olive-oil, a viscous 
mass of a grey colour is formed : this is an emulsion of mer- 
cury, consisting of a number of very small globules of the 
metal, each of which is coated with a film of oil kept adhering 
to it by molecular force. A fissure in the oil-film of one mil- 
limetre breadth will reunite with a force which, according 
to my own measurements, amounts to 6°09 mgr., and is there- 
fore comparatively great. In fact, an emulsion of this kind - 
will endure for months. The addition of an acid breaks up 
the oil-film, and consequently destroys the emulsion. So-called 
grey ointment is an emulsion of mercury in a highly viscous 
fat; its permanence increases with keeping, in consequence of 
the mercury forming with the rancid fat a compound (mer- 
curial soap ?) which appears to diffuse itself over the common 


_ surface of the two substances. 


Froth which may be seen ina solution of soap or in beer, is 
an emulsion of air in an aqueous fluid. Its permanence is 
greater in proportion as the original surface-tension of the 
pure liquid is decreased byan extraneous film on the free sur- 
face that is bounded by air. Homogeneous fluids containing 
no heterogeneous substance do not form a froth; it can be ob- 
tained from fatty but not from pure water. The force with 
which a rent of the breadth of a millimetre in the film of ex- 
traneous fluid on water tends to reunite, in the case of soap- 


312 On Emulsions, and the Action of the Bile in Digestion. 


solution is 5°58 mgr., of albumen 2°40 mgr., and of a ten- 
per-cent. solution of tannic acid 2°38 mgr. 

With organic fluid substances like albumen and solution of 
tannic acid, a thin membrane of the fixed substance seems to 
form on the surface of the air-bubbles; for they show angular 
protuberances, and the surface becomes less mobile ; this im- 
- mobile membrane promotes the durability of the emulsion. A 

permanent froth of this kind made with white of egg is well 
known in the kitchen. | | 
_ With very volatile liquids, or such as are easily soluble in 
the original aqueous fluid, such as alcohol and ether, the froth 
soon subsides; for the filin of extraneous liquid on the surface 
of the water rapidly disappears, owing either to evaporation 
or solution. The froth of beer is broken up by a small quan- 
tity of ether; for the tension of the common surface of 
that substance and air is very slight, and the surface itself 
tears under the dispersion of the fluid laminz forming the 
foam, in a similar way as in the experiments on the dispersion 
of soap-solution over the common surface of oil and water, 
described above (under 3), where particles are split off from 
the main mass of oil. 


8. Conclusions. 


(1) A solution of soap disperses itself over the common sur- 
face of oil and water. 

(2) This dispersion causes, in the interior both of the oil 
and the surrounding fluid, eddies or vortex-movements, by 
which particles of the oil are isolated or detached, and are 
drawn into the surrounding fluid, where they form small glo- 
bules. 

(3) Very minute quantities of soap, so small that they 
cannot even be recognized by the microscope, are enough to 
produce this dispersion-phenomenon and the movements in the 
whole body of oil caused by it. 

(4) Fixed oils containing free fatty acid form in a weak 
solution of soda a solid soap, which dissolves in the surround- 
ing fluid and is dispersed over the surface of the oil. : 

(5) With a certain concentration of the solution of soda, 
and a certain solubility of the soap that is formed, the disper- 
sion occurs at certain intervals, and detaches a large number 
of the small oil-globules. This explains the spontaneous for- 
mation of an emulsion observed by Joh. Gad, and the Amaba- 
like movements of the oil-globules in dilute solution of soda. 

(6) The globules of oil are coated with a thin film of soap, 
either solid or dissolved in water; and this film, by molecular 
action, causes the oil-surface to be less mobile, prevents the 


Photographic Method of Registering Absorption-Spectra, 313 


globules from coalescing, and materially promotes the dura- 
bility of the emulsion. 

(7) Apothecaries’ emulsions consist of oil-globules coated 
with a thin film of gum, which is retained at the oil-surface 
by molecular force, and prevents the small globules from co- 
alescing to form drops of oil. 

(8) In the case of castor-oil an emulsion cannot be readily 
formed, because the soap produced by the contact of the oil 
with the soda-solution is highly soluble. 

(9) Bile facilitates the solution of the solid soap, and on 
that account promotes the development of emulsion, in the 
fluid contents of the intestine, or under certain circumstances 
may impede it. But the mobility of the oil-surface is increased 
by the bile. 

(10) From the height of the ascent in capillary tubes, or 
from the behaviour of fluids at their common surface with air, no 
conclusions can be drawn as to the phenomena that will occur 
at their common surface with other liquids or with solid bodies. 

(11) Froth is an emulsion of air instead of one of oil. Its 
permanence depends on the same physical conditions as that 
of oil emulsions. 


XLIX. On the Photographic Method of Registering Absorp- 
tion-Spectra, and tts Application to Solar Physics. By 
Capt. W. DE W. Asney, #.2%., F.BS.* 


rgX\HERE are certain difficulties in registering the visible 

absorption-spectra as observed, dependent on the eye of 
the observer, and on his power of representing correctly 
what he sees; and it is owing to these deficiencies that 
curious mistakes have been made in endeavouring to draw 
absorption-phenomena. Up to the present time it has been, 
comparatively speaking, useless to attempt such registration 
by means of photography, owing to the fact that merely one 
part of the spectrum was impressionable by the silver salts 
eniployed as a sensitive medium. Since my discovery that 
silver bromide could be prepared in such a molecular state as 
to be sensitive to the whole spectrum (visible, ultra violet, and 
ultra red), the difficulty in the employment of photography 
is done away with; and it should be taken into use as much 
as possible, so as to eliminate the errors of eye-observations. 
A natural objection would arise at first sight, viz. that for the 


* Communicated by the Physical Society. 
{ Except those radiations of low amplitude and large wave-length 
which are emitted by bodies at ordinary temperatures. 


314 Captain W. de W. Abney on the Photographic 


different parts of the spectrum the sensitiveness of the silver 
compound is materially different, and that consequently the 
absorption at different parts cannot be well compared. ‘The 
objection vanishes, however, at once, if ordinary precautions 
are taken; and as an illustration I will take a case. 

The absorption of a violet (cobalt) glass was required to be 
registered photographically. A spectroscope having two 
prisms of 62° was judged to give sufficient dispersion; and a 
lens was used in the camera of a focal length of about 2 feet. 
This gave a spectrum about 4 inches long, including the 
visible and invisible radiations. The plate having been placed 
in the camera, the top half of the slit was shielded, and sun- 
light was reflected onto the bottom half for two minutes; the 
sunlight was diverted, and the absorbing medium (in this case 
_ violet glass) was placed in front of the slit*, the lower half 
covered up, and sunlight again reflected onto the top half of 
the slit for two minutes more. ‘The plate was then developed, 
and a print taken from the negative. A scale of shade having 
been prepared, the following diagram was drawn from the 
measurements made with it. : 

The top continuous curve of fig. I. shows the intensity pro- 


FlG.f 


FCP 


7 
1 
' 
I 
1 
1 
‘ 
1 
i) 
t 
1 
' 
1 
1 
i} 
t 


D y aera: TH 


RN 


duced on the plate by unscreened sunlight. The dotted line 
in the same figure shows the curve obtained when the cobalt 
glass is interposed. 

I would here remark that care is necessary not to introduce 


* When this paper was communicated to the Physical Society, Prof. 
Macleod suggested that the absorption of a liquid might be better demon- 
strated if a wedge-shaped vessel containing it were placed in front of a 
longer slit, of which a small image might be produced at the focus of the 
collimating lens. This is quite practicable, as Professor Macleod and my- 
self have found by actual experiment; and if the image of coloured liquid 
be corrected by a similar wedge of colourless liquid of nearly the same 
specific gravity, there is no inconvenience attaching to it. 


Method of Registering Absorption-Spectra. 315 


an error, as it must be remembered that the shades produced 
photographically have not the same gradations as the inten- 
sity of light, as Bunsen and Roscoe first showed. 

Fig. I. shows the absorption of the violet glass, on the pre- 
sumption that the intensity of the radiations 1s equal through- 
out the spectrum, an assumption which is very generally 
made. 

I have found that it is convenient in taking these spectra 
to modify this method. The absorption produced by potas- 
sium chromate takes somewhat of a wedge-form, shadmg off 
from darkness in the violet to total transmission at the least- 
refrangible end of the spectrum. Ifa dilute solution of this 
substance be interposed in each case between the source of 
light and the slit for half the time of exposure, we have an 
impression of the spectrum the varying intensity of which is 
less marked than if such an artifice be not employed. 

I may here remark incidentally that the passage of hght 
through an aqueous solution seems to interfere very little 
with the intensity of the photograph at the least-refrangible 
end. I had looked for a marked diminution, but have scarcely 
noticed it. 

In photographing these absorption-spectra the source of 
light should be brilliant: sunlight, the image of the incan- 
descent points of the electric light, or the oxyhydrogen light, 
may all be used; but I prefer sunlight, as we are enabled by 
the Fraunhofer lines to fix the locale of the absorption-bands 
more readily than with the other two. 

Another application of this method is to the solar spec- 
trum itself. Researches have shown that the bright-line 
spectra of incandescent compound bodies should lie in the 
least-refrangible end of the spectrum, and that to discover 
these a search must be made in these regions. As far as the 
visible spectrum is concerned such a search has been made; 
but we have yet to examine those regions which are invisible. 
At a low temperature it is quite possible that the compound 
bodies should give off vapours of the compound, whilst at high 
temperatures, such as that of the electric arc, they are pro- 
bably dissociated. If, then, we wish to ascertain the exist- 
ence of such compounds in the photosphere, we are driven to 
compare the solar spectrum with the bright-line spectra of the 
various compounds when heated at such low temperatures as 
those of the ordinary colourless gas- or spirit-flame. To pho- 
tograph portions of such spectra (even the most “actinic” 
region of the spectrum) is a feat of uncommon difficulty; and 
it would require hours, | might say days, of exposure to im- 
press lines in the red-region. Such an attempt would be 


316° Dr. A. Schuster on Spectra of Lightning. 


practically useless, as we can accomplish the same end in as 
many minutes by an indirect method as it would require hours 
by the direct method. 

_ The following illustration will show how it can be accom- 
plished. The top half of the slit is covered as before, and 
sunlight reflected onto it, and the spectrum is impressed 
on the photographic plate. The bottom half is next covered 
up, and a flame, in which the compound to be examined, is 
placed in front of the slit; the sunlight is then caused to tra- 
verse the flame, and a second spectrum is impressed on the 
plate through the top half of the slit. 

New absorption-lines are thus formed in the solar spectrum, 
or those already existent are intensified, as is already well 
known. Asan example, lithium chloride was heated in the 
flame, and the known line of lithium was found reversed be- 
tween B and OC, though absent in the spectrum of sunlight, 
and a faint line lying in the spectrum below the red was 
found intensified. By following out this plan we perhaps 
may eventually establish the existence of compounds in the 
solar photosphere. By using the light emanating from the 
white-hot carbon points of the magnetoelectric light to produce 
a continuous spectrum, and by burning the metallic compounds 
as before for one spectrum, and then by using sunlight to give 
the other spectrum, confirmatory evidence would be obtained. 
I may remark that I have photographed bright-line spectra of 
lithium, and got the same line in the ultra red as that obtained 
reversed. This method seems to promise to be a new weapon 
of attack in solar physics, more especially in this ultra-red 
portion. ; 


L. On Spectra of Lightning. 
By Axntuur Scuuster, Ph.D., F.R.AS.* 


Age observers of lightning-spectra agree in having seen 

the line-spectrum of nitrogen ; but most of them have 
seen, in addition to this, sometimes a continuous spectrum, 
sometimes a band spectrum, the chemical origin of which 
is unknown. 

The following historical summary may give an idea of our 
knowledge on that point. 

Prof. Kundt (Pogg. Ann. cxxxy. p. 315) observed a line 
spectrum consisting of one or two lines in the red, some very 
bright ones in the green, and some less bright ones in the 
blue. He mentions that the lines are not always seen together. 


* Communicated by the Physical Society, having been read at the 
Meeting on February 22nd. 


Dr. A. Schuster on Spectra of Lightning. 317 


Lines which in one flash appeared especially bright were not 
seen in another flash. The greater number of flashes, how- 
ever, gave a different spectrum altogether. In the place of 
bright lines a great number of bands were seen; and Prof. 
Kundt even distinguishes two different band spectra. 

Mr. John Herschel (Proc, R. S. xvii. p. 61) observed a 
variable continuous spectrum crossed by bright lines, which 
also had a variable intensity. He gives the measurements of 
two lines, which agree very well with nitrogen-lines. 

M. Laborde (Les Mondes, viii. p. 219) observed some lines, 
especially one near H, which sometimes appeared alone. He 
also saw a continuous spectrum. 

Dr. H.Vogel (Pogg. Ann. exliii. p. 653) describes lines only; 
but in his list I find two which do not coincide with ary bright 
lines in the spectrum of the electric spark taken in atmospheric 
air ; they do, however, coincide with two bands which I have 
observed in some flashes of lightning, as I shall show. 

Mr. J. P. Joule (‘ Nature,’ vol. xvi. p. 161) also observed 
some spectra of lightning. Frequently there was only one 
bright line visible, this being coincident with the brightest 
nitrogen-line. At other times there were several bright lines 
visible, sometimes with and sometimes without the green 
nitrogen-line. A continuous spectrum was also observed. 

Mr. H. R. Proctor (‘ Nature,’ vol. xvi. pp. 161 & 220) gives 
some measurements of lines which do not lay claim to any 
accuracy. He observed also a band spectrum, which he finds 
not to be the band spectrum of nitrogen. 

From conversation with Prof. A. Young, I learned that he 
also had seen a line spectrum, a band spectrum, and a conti- 
nuous spectrum. 

During my stay in Colorado last summer, I had some good 
opportunities of studying the spectra of lightning. It was 
my intention to get some reliable measurements of the band 
spectrum which I, in common with most observers, have 
seen; and in order to have greater chance of succeeding, I 
confined myself to one part of the spectrum only. The part I 
chose extended from 7%=5000 to A=5800, and covered, there= 
fore, most of the yellow and green. I used a direct-vision 
spectroscope, with a slit movable by means of a micrometer- 
screw. A bright line in the principal focus of the telescope 
formed a fiducial mark. Under ordinary circumstances, the 
slit is moved until the line to be measured forms a continua- 
tion of the bright line which reaches down into the centre of 
the field. I found, however, that the bands I wanted to mea- 
sure were nearly as broad as the thin glass bar which carries 
the bright line; and I used the bar therefore simply as pointer. 


Phil. Mag. 8. 5. Vol. 7. No. 44. May 1879. 2C 


318 Dr. A. Schuster on Spectra of Lightning. 


The measurements were always made at night; and the spec- 
troscope was left undisturbed until the following morning, 
when the Fraunhofer lines in the neighbourhood were mea- 
sured, so that the wave-lengths of the measurements could be 
interpolated. | 
It is of course impossible to put a pointer on a band during 
the instantaneous flash; but a succession of flashes allows us to 
put the pointer successively nearer and nearer until we see it 
in coincidence with the band. In this way several readings 
of each band were obtained. The dispersive power of the 
spectroscopes was such that, with a higher-power eyepiece than 
the one used in this investigation, the nickel-line could be 
seen between the two sodium-lines. The distance between the 
two sodium-lines was such that the two readings of the slit 
differed by ten divisions of the micrometer, or one tenth of a 
whole revolution. With sunlight I can measure easily to the 
tenth part of the distance between the sodium-lines. I ob- 
tained measurements on three different nights. Unfortunately, 
the best nights for the work occurred before the Total Solar 
Heclipse, which had taken me out to Colorado. A desire to 
save my eyes prevented me from making as good use of these 
nights as I otherwise should have done. 
July 25th, West Las Animas.—The whole horizon seemed to 
be almost constantly illuminated with lightning, generally sheet- 
lightning. I observed about thirty or forty different flashes. I 
often saw the bright nitrogen-lines 5002 and 5681. Idid not 
take any measurements of these lines; but there can hardly be 
a doubt as to their position. I saw in the part of the spectrum 
which I was observing three bands, which, however, did not 
always appear together. The measurements reduced to wave- 
lengths will be given further on. ‘Two measurements of the 
bands #8 and y were obtained, but one only of the bande. The 
greatest difference between the two measurements amounts to 
three times the distance between the sodium-lines. ‘This 
difference must be partly accounted for by the difficulty of 
the observation, partly by the fact that the spectroscope had 
only just been unpacked after the journey; and it was found 
next day that it was considerably out of adjustment. The 
micrometer-screw, also, owing to the heat and dust, had a 
considerable backlash ; it was taken to pieces next day and 
cleaned, which greatly improved it. | 
August 3rd, Manitou.u—Clouds were coming from the west 
over Pike’s Peak; and strong flashes of lightning, partly sheet 
lightning, partly forked lightning, were observed. Only two 
measurements were secured. One of the bands measured was 


&. Prof. Arthur Wright, who was present, observed that one 


Dr. A. Schuster on Spectra of Lightning. 319 


spot of the sky was illuminated during some flashes with a 
strong blue light, looking like a fluorescent light. I pointed 
the spectroscope to that spot, and observed a single broad band 
in the green. I moved the pointer on it as well as I could; 
but not being able to get another flash to verify the measure- 
ment, I had to take the reading. The position of this band, 
which I call 8, is very doubtful. 

August 18th, Salt-Lake City—I only obtained one mea- 
surement of the band y. The kind of lightning observed differed 
considerably from that of the preceding nights. The lightning 
was nearly all forked lightning; and the bright nitrogen- 
line came out very strongly. ‘The bands were but seldom seen. 
In one flash I saw a series of lines in the green which I had 
never seen before. My impression is that they were at about 
equal distances from each other, decreasing in strength towards 
the red; so that the whole made an impression similar to that 
of a fluted band, such as those seen in the spectrum of alu- 
minium oxide, but shading off towards the red. 


In addition to the line and band spectra, I have on many 
occasions seen a continuous spectrum only. 

The following Table contains all the measurements I have 
taken. I have added in the last column numbers contained 
in Dr. Vogel’s list of lines. It will be seen that these coincide 
with two of the bands I have seen. 


Band. | Date. AX _| Mean. | Vogel. 


ae | July 25 | 5592 | 5592 


| July 25 | 5348 
B. | July 25 | 5329 | 5334 | 5341 


am ef | —— 


July 25 | 5175 
y: July 25 | 5193 | 5182 | 5184 
Aug. 18 | 5177 


0. Aug. 3 | 5260 | 5260 


In trying to identify these bands with known spectra we 
meet with an unexpected difficulty. Two of them unfortu- 
nately admit of two different interpretations. At first sight 
I was struck by the close agreement of « and y with two bands 
of carbonic oxide. These bands fade away towards the blue; 
and their sharp edges have a wave-length of 5607 and 5197, 
Observing with the same spectroscope, and widening the slit 
as I did in observing the lightning, I can produce the same 
impression of an unshaded band; and taking a measurement of 

2C 2 


320 Dr. A. Schuster on Spectra of Lighindaget 


the centres of the bands under these circumstances, I obtain - 
X=5979 and A=5180, which agree within the limits of pos- 
sible errors with the above values. 

The ordinary spectrum of air, however, contains a band at 
5178; so that, as far as mere position is concerned, one might 
well be taken for the other. I was, however, under the im- 
pression that I had sometimes seen this band without the chief 
nitrogen double line 5002-5; and as the yellow band of car- 
bonic oxide was also apparently present, I stated with consi- 
derable confidence when I first wrote out this paper that I had 
observed the spectrum of carbonic oxide. It was only when 
I came to work out the position of the band 6 that I began to 
have serious doubts as to the accuracy of this conclusion. The 
position of the band 6, as I have said, is very doubtful ; I even 
thought it was possible that I had taken a very bad measure- 
ment of either 8 or y, and felt at first inclined to reject it alto- 
gether. On working out its wave-length, however, I found 
that it was coincident with one of two strong bands, which are 
found at the negative pole of vacuum-tubes filled with oxygen. 
Now the second of the two bands is nearly coincident with 
the yellow band of carbonic oxide; so that, of the two bands 
which I at first thought belonged to that gas, one might be 
due to nitrogen, the other to oxygen, as seen at the negative 

ole. | 
a The explanation of the band 8 is obvious. Itis the brightest 
of the two green lines in the low-temperature spectrum of 
oxygen. Its wave-length, when seen under a pressure of about 
a millimetre, is 5329; but under higher pressures it widens 
more on the less-refrangible side than towards the blue, and 
may well appear as a band with its centre at 5334 or even 
5341, as given by Vogel. ! 

I have not been able to obtain this band from atmospheric 
air in vacuum-tubes, although I have tried the experiment 
under various pressures. If the so-called continuous discharge 
is allowed to pass, the band spectrum of nitrogen alone appears; 
if the disruptive discharge passes, the high-temperature spec- 
trum of oxygen is superadded to the line spectrum of nitrogen. 
As regards the two bands a and ¥, it does not seem to me to 
be possible at present to decide between the two interpreta- 
tions which I have given. On the one hand, it seems impro- 
bable that the slight traces of carbonic acid known to exist in 
the atmosphere should reveal their presence in the spectrum ; 
but, on the other hand, it is to be remarked that oxygen 
vacuum-tubes, which show the band §, always reveal the 
slightest trace of carbonic oxide. It is exceedingly difficult, © 
though quite possible, to obtain the band.6 without the bands 


Mr. J. W. L. Glaisher on a Property of Vulgar Fractions. 321 


aandy. The measurement of 6, however uncertain, renders 
it probable that the spectrum of the negative pole in oxygen 
forms part of the spectrum of lightning; and on the whole I 
should feel inclined to attribute the band « to oxygen. I 
have shown in my paper on the spectrum of oxygen that this 
spectrum of the negative pole is due to an allotropic modifi- 
cation of oxygen (possibly ozone), and I have been able to 
obtain it, though only temporarily, in the positive part of the 
discharge. As regards the band y, I have some difficulty in 
attributing it to nitrogen, and still think it probably due to 
carbonic oxide. During the observations I certainly felt con- 
vineed that it did not belong to the same-spectrum as the chief 
lines of nitrogen, and I made a note that, on the contrary, it 
generally appeared together with 8. It seemed sometimes to 
be present alone, and often to form the most prominent part 
of the whole spectrum. As the lines of the capillary part of 
an oxygen-tube are also present at the negative pole, together 
with the bands distinctive of that pole, I can best express my 
observations on the band spectrum of lightning by saying that 
it resembles in a remarkable way the spectrum which is found 
at the negative pole of a vacuum-tube filled with oxygen which 
is slightly contaminated with carbonic oxide. 


LI. Ona Property of Vulgar Fractions. 
By J.W. L. GuaisHer, V.A., FLRS* 


§ 1. fs bine present paper relates principally to the following 

property of vulgar fractions :—lIf all the proper 
fractions in their lowest terms having numerators and deno- 
minators not exceeding a given number n, be written down in 
order of magnitude, then each of these fractions is equal to 
the fraction whose numerator and denominator are respectively 
equal to the sum of the numerators and denominators of the 
fractions on each side of it; for example, if n=7, the frac- 
tions are 


ft ft oh Sore week ~. 3).D Sb 3. 4° 5-6 
Pare s GO rae at ae oe ae 
and 
1. 2-2 ae ee Pe) eo 
= oi &e. 


6" Eo oe GE 4 BT? 

This property was enunciated by Mr. John Farey in the 
Philosophical Magazine for May 1816 (vol. xlvii. pp.885-386), 
and was shortly afterwards proved by Cauchy. ‘There is an- 


* Communicated by the Author. 


322 Mr. J. W. L. Glaisher jae 


other property of the fractions arranged in order of magnitude 
as above, viz. that the difference of any two consecutive frac- 
tions is equal to the reciprocal of the product of their denomi- 
nators; thus, for example, 


fd tlie 


6 12 6.7 (57 60h. 4 
The first property follows at once from this; for if si i s 
1 92 3 
be any three consecutive fractions of the series, so that 
99 Scag 2 ae 
bo by © baby bs bs = baby’ 
then 
gb, — ayo = il asDo —Ayb3= 1 3 
whence 
gb — dybg = azbo — (gb ° 
therefore 


do(b, +3) =b;(a, + as), 
V1Z. 
Coie ay +- As 


by 5p abs 


which is the first property. 

In the next two sections I give an elementary demonstration 
of these properties: §§ 4 and 5 contain an independent proof 
of the first property ; § 6 contains an extension of the circum- 
stances in which the properties are true; and §§ 7-16 are de- 
voted chiefly to their ey 


§ 2. Lemma. —If 5 be a proper fraction in its lowest terms, 


and if £, eo be the aed fractions, below and above, to = 
having denominators less than 6, then 


ptp'=4, qtq=b; 
and also 


BP, Pee 
By bo Ge 
For let 7 “ be converted into a continued pees and let £ be 


the taal convergent to : 


7? and suppose that a<5 ;, then 


b’ 
a puke 


6 i gq bg ‘ 
whence 
aq—bp=1. 


Property of Vulgar Fractions. 323 


Now if there be a fraction ~ (8<8) lying between ; and = 


then 


Se 6 Gt —g 
therefore 
rg—sp _ ag—bp 
Ss gat, aS 
gain 
b? 
that is, 
rq—sp< 53 


viz. a positive integer is less than a proper fraction, which is 
impossible. Therefore is the nearest fraction less than ; 
which a a denominator less than 0. 

Also, © = —P is the nearest fraction greater than ; “ which has 
zt aie less than 0b; for if - 45 <b) lie between : and 


(p then 


a— 
b—g 
Cet.) bp. 


mae — 9 


b—q 3 ~ b= b 


viz. 
a le inh as aq—bp 
s ep 
ft 
oe: 
or | 
as—ps—br+qr< 7 
which is impossible. 
The oe is exactly similar if the last convergent ’ be 


greater than ¢ 53 and therefore, always, if : be the last con- 
vergent to 5 ~, the nearest fractions to = 5200 each side, are pnd 


ae , whence the truth of the first part of the lemma is evident. 


Also since 
i poe Fi eppi a. 1 
b go bg ba b= Oaae 


B94 . Mr. J. W.L. Glaisher ona | 


it follows that if Pe a bb the nearest fractions to 2 ~, below and 


above, having denominators less than 6, then 
Sp sa. a 
bg by 
which is the second part of the lemma. 

§ 3. The properties enunciated in § 1 are direct conse- 
quences of the lemma; for if the series of fractions whose 
numerators and denominators donot exceed n be written down 
in order of magnitude, and if the fractions with the denomi- 


nator n+1 be ae in their proper Pe in ue series, then, 
if the fraction 


as i be inserted between © EB * and a ~2 we have, by 


the second part of the lemma, 
m =) 1 Ay m 1 


Sj =) SS ee SS ae 


ae Geb 6 n+l eG. 


ay a 
for x 5 are the nearest fractions, below and above, to 
1 2 


: ‘ 1 Saas n 
having less denominators than n+1. Also ca and ee 
will appear at the beginning and end of the series, and 

i ee ae n .... n= 
n ntl n(n+l1), n+1 n  (n+1)n 
Thus if the second property be true for all the fractions in the 
original series, it still remains true after the fractions with 
denominator »+1 have been inserted. It can be at once veri- 
fied that the property is true for n=2, 3, &e.; and therefore it 
is true generally. Thus the second property is proved; and 
the first property, which is a consequence of it, is therefore 
proved also. For example, if n=6, the series of fractions is 
LA Le de 2 3 ee 
Grob 145 351) 2,03 4oa 


when the fractions with denominator 7 ane introduced, : ap- 


soe: 
mee iy 


a Bike 1 oon 
en at the beginning, 7 between i al 3 7 between F and 9? 


= = between : and ee 2 between : and = and : at the end. 
Kince 7 is the largest denominator, the second property is true 
(by the lemma) for all fractions in which this denominator is 
involved; so that if the property is true for n=6, it is true 
. for n=%. 


Property of Vulgar Fractions. 325 


It is evident that the new fractions make their appearance 
at the beginning and end, and between each pair of fractions 
which are such that the sum of their denominators is equal to 7; 
and, generally, in the series of fractions whose numerators 
and denominators do not exceed n, the fractions with deno- 
minator n+1 make their appearance between eech pair of 
fractions which are such that the sum of their denominators is 
equal to n+1. If, therefore, d(n) denote the number of 
numbers less than n.and prime to it (unity included), there 
will be d (n+1)—2 such pairs of fractions; and the corre- 
sponding sums of numerators will be the {¢(n+1)—2} num- 
bers which are less than n+ 1 and prime to it, unity and n being 


| ii n : 
excluded, as these correspond to ary and Pata which appear 


at the beginning and end of the series. 

At the beginning of the series of fractions there will be 
several with unit numerators; if the greatest numerator or 
denominator be uneven, =2n+1, then the series will be 


Leh 1 Pty 
Intl AW n+l @n-+l rn’ 


viz. the first fraction that has not a unit numerator will be 


2 SN Ss 1 1 
me? and this will appear between met and 73 8° that there 


will be n+1 fractions with unit numerators at the beginning ; 
and, of course, since the second half of the series of fractions 
is complementary to the first half, the last n+1 fractions will 
have numerators differing from their denominators by unity. 
If the greatest numerator or denominator be even, =2n, the 


first fraction whose numerator is not unity will be , and 


2 
this will appear between - and si 2° that in this case 
there will be at the beginning n+1 fractions with unit deno- 
minators, and at the end the same number of fractions with 
numerators differing by unity from their denominators. 

§ 4. The first property may also be proved directly, by means 
of the first part of the lemma, without the intervention of the 
property relating to the difference of two consecutive fractions, 
in the following manner. 

It is convenient to have a name for the two fractions nearest 


to = below and above, having denominators less than b; and 


these will therefore be referred to in this section as respectively 


326 Mr. J. W. L. Glaisher on a 


the inferior and superior convergent of : , or as the conver- 
a 
a 
each side of it, have denominators less than 6, then by the 


/ 
lemma they are the two convergents £, P of 2, 
dq oo 


gents of If in the series of fractions the two next to A on 


and 
ptp'=a, qtq=b. 


/ 
In the general case, let @ 2 be respectively the inferior and 


7 
superior convergents of = , and let ~) = be the two fractions 
which stand next to - below and above, in the series of frac- 


tions, v and 2’ being supposed greater than b; so that the 
series of fractions is 


LENE TS AS age 
oe He ed gf | 
By the first part of the lemma the convergents of = are ; and 
U—-a . LO ae u—2a 
om! f v—b>b, the convergents of pap tes and ee 


if v—2b>b, the convergents of wee are ; and = , &e. 
Suppose that »—(m—1)b>, but that v—mb <b (4. e. suppose 
that v >mb and <(m-+1)d); then we must have v—mb=q and 
u—ma=p; for v—mb is the first denominator less than } 


e ° e ° Cet a 
which occurs in the descending series of fractions from z3 and 


this is in fact the definition of gq. aes 
Similarly in the ascending series, we have g/=v’—nb, 
pl =u —na if v' >nband <(m+1)b. Alsop+p’=a,q+q=6, 
and therefore 
(w—ma) + (wu! —na)=a, 


(v—mb) +(v'—nb) =); 


whence 
utu=(m+n+l1)a, 


v+e’=(m+n+1)b; 
so that 
utu’ _@ 


tty ~~ b 


sr re Ati ema” eee 
ssi 


Property of Vulgar Fractions. 327 


DB og cae 
If = eet ae 7” we merely have the case of m=0 or n=0 
respectively. 

It is evident from the preceding considerations that p, q, 
oa numerator and denominator of the inferior convergent of 


- are the remainders when w and v are divided respectively 
by a and b; and that p’,q’, the numerator and denominator of 


the superior convergent ate 7) are the remainders when wu’ and 
v’ are divided by a and b. 

It was rather more convenient to define the convergents of 
; as the fractions nearest to it, on each side, having denomi- 
nators less than b: but they might equally well be defined as 


the fractions nearest to 5s on each side, having numerators not 
exceeding a; oe the single case of a=1 excepted, if 2 be a 


convergent of S, then p> or <a, according as g> or <b. 


b? 

§ 5. The following ten consecutive fractions, which be- 
long to a series in which the greatest admissible numerator or 
denominator is 1000, will serve to illustrate the remarks in the 
last section :— 


ftp to 20 IT 22 OG 


a === =) ———9 a = aa e, ——4 =F — 
. 


220° 817 597 974 B77’ 911’ 534 691’ 848” 157 


Consider the fraction sss; we have 


12 
377 

814+29 60 5.12 
9744911 1885 5.877? 


so that the factor 5 divides out from both numerator and de- 
nominator. ‘To see how this is brought about by means of the 


lemma, we observe (i) that the conyergents of at ar a 


ibs) 19 i fee re 

597 S00 atl a oe 
29 12 17 

(ii) that the convergents of —— oi 2 * Bra 8 and 530? and that 


7 12 
the convergents of =— 594 We arz a a 7 3 


12 7 5 pret 
vergents of 377 We a5 and 157° Thus, considering the nu- 


and and that the convergents of =~ 


(iii) that the con- 


328 Mr. J. W. L. Glaisher on a- 


merators alone, the equations given by the lemma are, from Gi) 


af 12 9. 
19=1247; 
whence 
: “3 2 ne ie 
Similarly, from (ii), ie 
20a sy 
: 17=12+5; 
whence a 
7 29=2.12+4+5, 


and therefore 


314+29=4.124(74+5)=4.12412 from (iii), =5.12. 
And similarly, for the denominators, from (i), 


974=3774+597, 997=3774 220; 
from (ii), | 

911=377+4534, 5384=377+4157; 
from (iil), 

290 +157=377; 
whence 

974+ 911 =5. 377. 


Also, the numerators 7, 5 of the convergents of Ee are the 


remainders when 31 and 29 are divided by 12; and the deno- 
minators 220, 157 are the remainders when 974 and 911 are 
divided by 377. 

The following example, also taken from the same series, 
affords another illustration of the relations connecting the frac- 
tions :— 


90° Aq. OF 61 84. 41. 48° 55 eee 


§ 6. The reasoning of § 3 shows that the two properties 
are still true in the more general case in which the series con- - 
sists of fractions in their lowest terms, having numerators not 
exceeding any given number m and denominators not exceed- 
ing any given number n, m being of course not greater than n. 
For consider only the second property (which includes the 
first), and suppose this property to be true for the series of 
fractions having numerators not exceeding m and denomina- 
tors not exceeding m+7r. Introduce the fractions having nu- 
merators not exceeding m and denominators equal tom+r+1; 
then, as in § 3, the property is true for all the fractions up to 


Property of Vulgar Fractions. 329 


the fraction next greater than in magnitude, and 


m 
mt+r+1l us 
the series of fractions greater in magnitude than Gee 
remains unaffected. Thus if the property is true for denomi- 
nators not exceeding m+v7, it is true for denominators not 
exceeding m+r+1. But it is true for denominators not ex- 
ceeding m or m+1, and is therefore true generally. 

If, therefore, in any such series as those considered in §§ 1-5 
all the fractious having numerators exceeding any given num- 
ber be removed, the properties will still hold good for the 
series of fractions that remain. For instance, if in the ex- 
ample at the end of § 5 the fractions having numerators 
exceeding 45 be removed, there remains the series 

Peete 4A ATE 7 
Bes ao 515 | 627 106" 
for which the properties are true. 

§ 7. I come now to the history of the properties stated in § 1. 
The first property was published by Mr. John Farey, in a 
letter to the Philosophical Magazine (vol. xlvii. 1816, pp. 385- 
386), entitled “ On a curious Property of Vulgar Fractions.’’ 
This letter commences :—“ On examining lately, some very 
curious and elaborate Tables of ‘ Complete decimal Quotients,’ 
calculated by Henry Goodwyn, Esq. of Blackheath, of which 
he has printed a copious specimen, for private circulation 
among curious and practical calculators, preparatory to the 
printing of the whole of these useful Tables, if sufficient en- 
couragement, either public or individual, should appear to 
warrant such a step: I was fortunate while so doing to deduce 
from them the following general property.” Mr. Farey then 


states the first property, viz. that if = = - be three conse- 
1 02 O% 
cutive fractions, then Sao eat Ge , and illustrates it in the case 
by by +63 


where the greatest denominator is 5. He concludes with the 
words, ‘‘ I am not acquainted, whether this curious property of 
vulgar fractions has been pointed out? ; or whether it may 
admit of any easy or general demonstration ?; which are points 
on which I shall be glad to learn the sentiments of some of 
your mathemetical readers.” 

An account of the property appeared under the title “ Pro- 
priété curieuse des fractions ordinaires,”’ in the Bulletin des 
Sciences par la Société Philomatique de Paris for 181 6, 
p- 112*. An examiple is given in which the greatest denomi- 

* By an error of paging, the page-numbers 105-112 oceur twice, and 


p. 121 follows the second p. 112. It is the first p. 112 that is here ye- 
ferred to. 


330 - Mr. J. W. L. Glaisher on a 


nator is 7. The property is stated to be taken from the Phi- 
losophical Magazine for May 1816; but Mr. Farey’s name is 
not mentioned. ) 

A proof was given by Cauchy in the same volume of the 
Bulletin (pp. 183-135), under the title “ Démonstration d’un 
théoréme curieux sur les nombres ;’”’ this proof was reprinted 
in t. 1. (1826) pp. 114-116 of his Ezercices de Mathématiques. 
The first three paragraphs of the paper in the Bulletin 
are :— 

“On trouve dans le dernier Numéro de ce Bulletin ’énonceé 
(une propriété remarquable des fractions ordinaires observée 
par M. J. Farey. 

“Cette propriété n’est qu’un simple corollaire d’un théoréme 
curleux que je vais commencer par établir. 

“ Théoréme.—Si, aprés avoir rangé dans leur ordre de gran- 
deur les fractions irréductibles dont le dénominateur n’excede 
pas un nombre entier donné, on prend a volonté, dans la suite 
ainsi formée, deux fractions consécutives, leurs dénominateurs 
seront premiers entre eux, et elles auront pour différence une 
nouvelle fraction dont la numérateur sera l’unité.” 

Cauchy thus discovers for himself and proves the second 
property, viz. that a — = = ae and deduces the first, or Mr. | 

Oe a 0904 
Farey’s, property fromit. Itis clear, from the first paragraph 
of his paper, that he must have referred to Mr. Farey’s ori- 
ginal letter in the Philosophical Magazine, since, as has been 
mentioned, Mr. Farey’s name does not occur in the account 
in the Bulletin. 

§ 8. In the ‘ Educational Times’* for 1868 Mr. C. W. Mer- 
rifield proposed the question, “ Mr. Henry Goodwyn published 
in 1818 a table, in which all proper fractions (reduced to their 
lowest terms) in which the denominator did not exceed 100, nor 
the numerator 50, were arranged in order of magnitude. He 
observed the following property, a general proof of which is 
N, N, N; 
Dy’ D,’ Dy 
and indicated a mode of solution depend- 


required. Let any three consecutive fractions be 
Ni Ns ee 
then Dip by : 
ing on the property D,N,—D,N,=1: a solution was also given 
by Mr. Morgan Jenkins. 
Probably all the proofs of the second property depend ulti- 
mately on the same principles. In the proof in §§ 2 and 3 an 
attempt has been made to render the analysis as elementary 


*®* Mathematical Questions with their Solutions. From the ‘Educational 
Times,’ vol, ix. pp. 92-95. 


Property of Vulgar Fractions. 331 


as possible. All that is assumed is that if P be the last con- 
vergent to r then ag—bp=+1. Itis a well-known theorem, 
and one given in elementary treatises on algebra, that any 
convergent to a fraction is nearer to it than any other 
fraction having a less denominator than that of the con- 
vergent ; and the proof* of this includes a proposition proved 
in § 2, viz. that P is nearer to ; than any fraction on the 
same side of it having a less denominator than 6. But it was 
more convenient to establish the result in § 2 independently, for 
the sake of completeness, as in any case it must have been 


shown that ae was nearer to 7 than any fraction on the same 
side of it having a denominator less than b. The lemmain § 2, 
which really forms an interesting theorem, cannot of course be 
new, but it is certainly little known. I may mention that, as 
far as lam aware, the only complete investigation of the theory 
ea 
given fraction, is given by Professor H. J. 8. Smith in the 
addition to his “‘ Note on Continued Fractions” (‘ Messenger of 
Mathematics,’ vol. vi. (May 1876) pp. 7-14). 

§ 9. Mr. Henry Goodwyn, who is referred to by Mr. Farey 
in his letter in the Philosophical Magazine (see § 7), pub- 
lished in 1818 a quarto tract entitled “ The first Centenary of 
a Series of concise and useful Tables of all the complete decimal 
quotients, which can arise from dividing a unit, or any whole 
number less than each divisor, by all integers from 1 to 1024. 
To which is now added a tabular series of complete decimal 
quotients for all the proper vulgar fractions of which, when in 
their lowest terms, neither the numerator, ror the deno- 
minator, is greater than 100: with the equivalent vulgar 
fractions prefixed. By Henry Goodwyn. London: 1818.” 
There is an introduction (pp. v—xiv), followed by the first 
centenary itself, which occupies pp. 1-18. Then there is a 
fresh title-page for the “ Tabular Series,’ which consists of pp. 
lii—vii (introduction), pp. 1-15 (the tabular series itself), and 
pp- 17-30 (appendix). : 

In 1823 Mr. Goodwyn published two octavo works, viz.:— 
(1) “A tabular Series of decimal Quotients for all the proper 
vulgar fractions of which, when in their lowest terms, neither 
the numerator nor the denominator is greater than 1000. 


* Todhunter’s ‘Algebra,’ art. 610; Gross’s Algebra,’ art, 149, 


of the successive minima of the expression 0, 0 being a 


332 Mr. J. W. L. Glaisher on a 


bears Mr. Goodwyn’s name. The ‘Table of Circles’ was 
subjoined to the ‘ Tabular Series’ of 1823, but sold also as a 
separate publication”. | 

§ 10. The ‘ Tabular series’ of 1823 contains the first eight 
(and occasionally nine or even ten) digits of the decimal values 
of all fractions having both numerator and denominator not 
exceeding 1000 arranged in order of magnitude, from 755 
to 6°, (1. e. of those whose decimal values begin with ‘0). At 
the conclusion is “ End of Part I.;’’ and it was the author’s in- 
tention that Part II. should contain the fractions whose decimal 
values begin with:1, Part III. those beginning with ’2, Part LV. 
with °3, and Part V. with 4. Parts I-V. would thus contain 
the decimal values of the fractions up to 4; and it would be 
unnecessary to print the other half of the table, as the argu- 
ments and results would be complementary to those in the first 
half. Part I. is all that was published. 

The ‘ Table of Circles ’ (1823) contains all the periods or 
“ circles”’ of the fractions having denominators prime to 10, 
from 1 up to 1024. 

By means of the two tables the complete decimal value of 
every vulgar fraction less than 755 having in its lowest terms 
a denominator not exceeding 1000 may be obtained at once. 
For example, from the ‘Tabular Series’ we find3, =-07918552; 
and entering the ‘Table of Circles’ with 221 (i. e. with the 
residual factor of the denominator when powers of 2 and 5 
have been thrown out) we can complete the period from among 
the “circles ’’ of 221, by means of the “‘ circle” which contains 


the digits 7918552, which is -9909502262443438914027149 


32126696832579185520361, so that the remaining digits of 
the period are 036199... 8325. | 

The ‘ Tabular series’ of 1818 is similar to that of 1823, but 
only includes fractions having both numerator and denominator 


* Introduction to Tabular Series (1823), p. iv. 


Property of Vulgar Fractions. 333 


not exceeding 100, up to $ ; and the ‘ Table of Circles ’ which 
accompanies it only extends to 100, and occupies but one page. 
The ‘ First Centenary ’ itself * contains tables for the conver- 
sion of vulgar fractions into decimals, arranged by denomi- 
nators instead of in order of magnitude as in the ‘ Tabular 
Series.’ | 

§ 11. The arguments in the ‘ Tabular Series’ of 1823 afford 
a beautiful illustration of the properties stated in § 1; and it 
is from this work that the examples in § 5 have been taken. 
It is very interesting to apply the reasoning of § 4 to groups 
of fractions as they stand in this Table; of course in § 5 it 
was convenient to select examples in which only a few frac- 
tions were involved. Mr. Goodwyn writes in the preface to 
the ‘ Tabular Series’ of 1823 (p. iv) :—“ The Computer would 
draw the attention of the curious in such matters to the fol- 
lowing remarkable property of the fractions which form the 
Series: viz. In any three consecutive vulgar fractions in the 
table if the numerators of the extremes and the denominators 
respectively be added together, the sum will form the numerator 
and the denominator of a fraction equal to the mean.” 

On pp. iv—v of the ‘ Tabular Series’ attached to the ‘ First 
Centenary ’ of 1318, Mr. Goodwyn enunciates both properties. 
He explains that the fractions do not form an arithmetical 
progression, and proceeds:—“ In fact, the law of the increase 
is such, that each Fraction exceeds that which immediately 
precedes it by a part equal to unity divided by the product af 
their two denominators: so that the increment is anything but 
constant. The law, however, is invariable; and from it a 
ready method is derived for verifying the arrangement of the 
TABULAR, or any similar, SERIES.”’ 

He then refers to the mode of arrangement of the fractions 
(which are printed zigzag fashion in two columns), and con- 
tinues :—“‘ At the same time, it serves to illustrate this other 
law in the succession of the terms of the entire Series; namely, 
that the numerator of any Fraction in it is always the same 
aliquot part, or submultiple, of the sum of the numerators of 
the Fractions immediately preceding and immediately following 
it, which its denominator is of the swm of their denominators : 
... lt | the “Tabular Series’ ] may be curtailed, either by striking 
out all the Fractions that are of a given denominator, or by 
obliterating all those of which the denominators exceed a 
given denominator ; but, while, in the latter case, both the 


* It is to be observed that the title of the tract of 1818 is “The First 
Centenary .... to which is now added a Tabular Series .... ” (see title 
in §9); so that the ‘First Centenary’ of 1818 contains both the ‘ First 
Centenary ’ itself and also the ‘ Tabular Series.’ 


Phil. Mag. 8. 5. Vol. 7. No. 44. May 1879. 2D 


334 Mr. J. W. L. Glaisher on a 


laws, which have been mentioned, will remain unaffected, in 
the former case, neither of them will hold throughout the 
remaining terms.”’ 

§ 12. In his letter quoted in §7, Mr. Farey speaks of 
** some very curious and elaborate Tables of ‘ Complete decimal 
Quotients ’ calculated by Henry Goodwyn... .of which he 
has printed a copious specimen for private circulation... .” 
This appeared in the Philosophical Magazine for May 1816, 
and would seem at first sight to point to the publication of a 
specimen of the ‘ Tabular Series’ previous to this date. A 
copy of the specimen alluded to is in the library of the Royal 
Society. It contains the ‘ First Centenary’ only; and the 
following address is prefixed :— The Calculator of about a 
Chiliad of Tables, from the application of which, in various 
ways, he has himself derived considerable benefit, has been 
induced to print the annexed Centenary as a Specimen. Hn- 
couraged likewise by Friends—not, perhaps, quite impartial, 
—to give them some publicity, yet still doubtful in himself 
whether they deserve general notice, he adopts this method, 
which, he trusts, will not be deemed obtrusive or impertinent, 
of presenting this portion of his labours to a few Individuals. 
To these Gentlemen, indeed, he has not, in all instances, the 
good fortune of being personally known, but their scientific 
knowledge and mathematical attainments are highly and 
justly appreciated ; and, it is hoped, that amongst them, some 
will have leisure, and inclination, to honour him with their 
* sentiments on the Specimen, which is thus submitted to their 
consideration ; since he is anxious to confide to their decision, 
whether the Tables themselves are worthy of publication,—or 
may sink into oblivion with their Author. 

‘* As the above is a private Address, it seems needless for 
him to add, that the name of anyone, who may favour him 
with his opinion, shall not be divulged without his express 
consent. Hy. Goopwyn, Blackheath, Kent, March 5th, 1816.” 

The ‘ First Centenary’ (pp. xiv+18) is exactly similar to 
the ‘ First Centenary’ of 1818; and as the fractions are not 
arranged in order of magnitude, it contains nothing that in 
any way suggests either of the properties that form the subject 
of this paper. It seems pretty clear that no part of the 
‘ Tabular Series’ was published previous to 1818; for the title- 
page to the tract of 1818 runs “ The First Centenary ... to 
which is now added a Tabular Series ...;’? and the introduction 
to the ‘Tabular Series’ (1818), commences, “ Since the ‘ First 
Centenary, &e.’ and its Introduction were printed, which was 
in March, 1816, it has appeared to the Calculator... .” 

It would thus appear that Mr. Goodwyn published no Table 


Property of Vulgar Fractions. 339 


for the conversion of vulgar fractions into decimals, in which 
the fractions were arranged in order of magnitude, prior to 
the ‘ Tabular Series’ of 1818 ; and in this work both the pro- 
perties are referred to. In the ‘ Tabular Series’ of 1823 only 
the first is stated. The wording of Mr. Farey’s letter implies 
that he had seen not only the printed specimen of 1816, but 
also Mr. Goodwyn’s manuscript Tables. It is not clear, how- 
ever, whether Mr. Farey discovered the property he enunciated 
without any assistance from Mr. Goodwyn; or whether, Mr. 
Goodwyn having remarked the property as holding good in 
the ‘ Tabular Series,’ 7. e. when the denominator is 100, Mr. 
Farey merely extended it to the general case of any denomi- 
nator. Whoever first began to arrange the fractions in order 
of magnitude could scarcely fail to notice both properties ; and | 
the second, which relates to the difference of two consecutive 
fractions, would probably present itself first. On the whole, 
therefore, it seems most probable that only the extension to 
the general case was due to Mr. Farey. In none of Mr. 
Goodwyn’s works is any allusion made to Mr. Farey or to 
Cauchy. _ 

It seems curious that so elementary and remarkable a pro- 
perty of fractions should not have been discovered until 1816. 
It may of course be found that it had been published previously; 
but supposing the discovery to be due to Mr. Goodwyn and 
Mr. Farey, an explanation might be afforded by the fact that 
the ‘ Tabular Series ’ is probably the earliest Table of the kind, - 
and that the property would not be likely to present itself to 
any one who had not arranged a complete series of proper 
fractions having denominators less than a given number in 
order of magnitude. 

§ 13. Mr. Goodwyn’s works are almost unknown; and those 
of 1823, which are the most important, are, as mentioned in 
§ 9, anonymous. The only references I have seen to them 
are contained in Mr. Merrifield’s question quoted in § 8, and 
in De Morgan’s articles on Tables in the Penny and English 
Cyclopeedias. In the latter the works of 1823 only are de- 
scribed, and by inadvertence the ‘Tabular Series’ is stated to 
contain all fractions “‘ which in their lowest terms have a 
numerator not exceeding 99, and a denominator not exceeding 
1000, in order of magnitude.” In the Hnglish Cyclopedia 
(1861) De Morgan continues: —“ Mr. W oolgar is our authority 
for saying that there was a previous work by. Goodwyn, ‘ First 
Centenary of concise and useful Tables of Decimal Quotients ’ 
(1818) 4to. Mr. Goodwyn (of Blackheath) was an indefati- 
gable calculator; and the preceding Tables are the only ones of 
the kind which are published. | His manuscripts, an enormous 

2D 2 


336 Mr. R. 8. Brough on the proper Relative Sectional 


mass of similar calculations, came into the possession of Dr. 
Olinthus Gregory, and were purchased by the Royal Society 
at the sale of his books in 1842.”” Nothing is known of them, 
however, at the Royal Society. The Cambridge University 


Library contains two copies of each of Mr. Goodwyn’s publi- 


cations of 1818 and 1823*, but no copy of the specimen of 
1816. There is an account of Mr. Goodwyn’s works in the 
British Association Report on Tables (Bradford, 1873, pp. 
31-33), where I have erroneously attributed the property 
enunciated by Mr. Farey to Cauchy. A more complete de- 
scription of Mr. Goodwyn’s works 1s contained In a paper 
“ On Circulating Decimals, with special reference to Henry 


Goodwyn’s ‘ Table of Circles’ and ‘ Tabular Series of Decimal _ 


Quotients’ (London, 1818-1823),” printed in the ‘ Proceed- 
ings of the Cambridge Philosophical Society, vol. iii. (1879) 
pp. 185-206. 


Trinity College, Cambridge. 
February 1ldth, 1879. 


LII. On the proper Relative Sectional Areas for Copper and 
Tron Lightning-Rods. By R. 8. Brovexy. 


O far as mere conductivity is concerned, a comparatively 
thin wire of either copper or iron would suffice for the 
loftiest conductor ; but such a thin conductor would be dan- 
gerous, because it would be fused by a heavy discharge of 
lightning. Now the problem is to determine what relative 
sectional areas should be given to copper and iron rods, in 
order that neither should be more liable to fusion than the 
other. 
The usual answer given is, that an iron rod should have four 
times the sectional area of a copper rod}. The result is, I 
suppose, arrived at in the following way. The conductivity 


* One of the copies of the ‘First Centenary’ (1818) contains the fol- 
lowing letter, “September 16th, 1831. Mrs. Catherine Goodwyn presents 
to the Library of the University of Cambridge a complete set of the works 
of her late father, Henry Goodwyn, Esq., of Blackheath, Kent. Royal 
Hill, Greenwich.” Mr. Goodwyn also published a few folding sheets on 
weights and measures &c., which are bound up at the end of this copy of 
the ‘ First Centenary.’ | 

+ Communicated by the Author, having been read before the Asiatic 
Society of Bengal in November 1878. 

a i seals Memorandum by General Sir Frederick Chapman, R.E., 


~ 


Areas for Copper and Iron Lightning-Reds. 337 


of copper is about six times as great as that of iron; but the 
melting-point of iron is about 50 per cent. higher than that of 


copper; therefore = =4 is the ratio for the sectional area of 
iron to copper. 

This simple treatment of the problem, however, is incom- 
plete, because it neglects to take three most important factors 
into consideration—namely (1) the influence of the rise of 
temperature in increasing the electrical resistance of the metal, 
(2) the difference between the “thermal capacity ”’ or “ specific 
heat’ of copper and iron, and (8) the fact that, the iron rod 
being made several times more massive than the copper rod, 
it will require a proportionately greater quantity of heat to 
increase its temperature. These omissions introduce an enor- 
mous error in the result. 

The effect of the passage of a discharge of lightning through 
the rod will be to raise its temperature. 

The temperature (T) to which a given length of the rod 
will be raised will depend on :— 

(1) The quantity of heat developed by the discharge. 

(2) The mass of the rod. 

(3) The specific heat o of the metal composing the rod. 

This may be expressed mathematically as follows: 


H 
T= const — ; 
om 


where m is the mass of a unit length of the rod, which we 
shall assume to be uniform in sectional area throughout its 
length, and H is the quantity of heat developed by the dis- 
charge. 

We may take c=0°1013 for copper, and o=0-1218 for 
iron. ‘These figures were only verified, by Dulong and Petit, 
up to 300° C. It is probable, however, that their ratio, with 
which we are only here concerned, would not greatly alter at 
higher temperatures. At any rate, comparing the specific 
heats between 0° and 100° C. with those between 0° and 800° 
C., we infer that any alteration would be in favour of iron, 7. e. 
that the specific heat of iron would increase in a quicker ratio 
than that of copper. 

Adopting the centimetre as the unit of length, the mass of 
one centimetre of the rod =pa, where a is the sectional area 
of the rod in square centimetres, and p=8°9 for copper, and 
p—-o for iron. 

Further, assuming the quantity and duration of the dis- 
charge to be constants, H = const x R, where R is the resist- 
ance of the unit length of the conductor. 


838 Sectional Areas for Copper and Iron Lightning-Rods. 


But R= = where A is the specific resistance of the metal 


per cubic centimetre at its temperature of fusion. 

We may take the melting-point of copper as 1400° C., and 
that of wrought iron as 2000° C.*, and, in order to find A, 
assume that Dr. William Siemens’s formula, which he verified 
to 1000° C., holds good, viz. 


Ne=Ao(0°026577 ¢2 + 0:0031443 ¢—0°29751) for copper, 
Ng= (0072545 #3 + 00038133 t—1-23971) for iron. 


The temperature ¢ in these formule is to be measured from 
the absolute zero; so that we have ¢=1673 for copper, and 
#=2273 for iron, | 

The value of Ay per cubic centimetre of copper is 1°652 mi- 
crohm, and per cubic centimetre of iron is 9°827 microhmsf. 

Thus the value of Az per cubic centimetre of copper becomes 
about 10 microhms at 16738° C., and per cubic centimetre of 
iron becomes about 107 microhms at 2273° C. 

Hence | 


Ei const=— for copper, 


and 
H= const =~" for iron. 
Therefore 
eee aoe ea iris 0 
Hy 2 OMMIS KB Vice? ae 
and 
es ey ation See 1G for iron. 


071218 x 7:8 x A? 
Now, putting T= temperature of fusion in each case, 


1400 = const ae ? for copper, 


2000= const —— for iron. 


Therefore 
Ne AAO O A263 
) ~ 2000 11-09 
=i alle 
whence A 8 
a nearly ; 
* Rankine’s Tables. + Bakerian Lecture, 1871. 


t Jenkin’s Cantor Lectures, from Mathiessen’s experiments. 


| 
| 


On the true Wave-length of a Cylindrical Resonant Tube. 339° 


or, the sectional area of an iron rod should be to the sectional 
area of a copper rod in the ratio of 8 to 3. 

This result is an argument in favour of the use of iron as 
being the less expensive. 

Calcutta, March 3, 1879. 


LIT. Experiments for determining the Correction to be added 
to the Length of a Cylindrical Resonant Tube to find the true 
Wave-length, and the Velocity of Sound in small Tubes. 


To the Editors of the Philosophical Magazine and Journal. 


GENTLEMEN, 
| BEG to submit to your consideration for publication the 
accompanying memorandum of experiments made by me 
with the object of determining the correction to be added to 
the length of a cylindrical resonant tube to find the true 
wave-length, and the velocity of sound in small tubes. 

They give results, as regards the first point, in the main 
confirmatory of those already arrived at by Lord Rayleigh 
and Mr. R. H. M. Bosanquet; but the methods of experi- 
ment followed by me being different to theirs, the notes may 
be of interest. As regards the second point I am not aware 
of any experimental results having been published. 

Iam, Gentlemen, 
5 1 Nab cea te Yours obediently, 

anonpur . 

March 22, ae. D. J. BLAIKLEY. 

The first method of experiment adopted by me is applica- 
ble only to tubes closed at one end, and consists in determin- 
ing in a tube of indefinite length the positions of the first and 
second nodes of a wave excited by a fork held over its mouth, 
the tube having one end sunk in water, and the water-level 
at the position giving maximum resonance determining the 
position of the node. The tube used was made of thin brass, 
and had an internal diameter of 2°08 inches; it was slung 
with a pulley and counterweight over a deep vessel of water, 
and its height out of the water at each observation read off by 
a scale. The advantage of the use of water instead of a sliding 
solid plug is that there is not the slightest noise to interfere 
with the appreciation of the point of maximum resonance. 

The forks used were ¢ 253°55 vibrations, e 817-3, g/ 
380°625, UP’ 444°5, and ¢” 507-2 Of these I had an oppor- 
tunity of comparing all but the e’ with Scheibler’s standards 
in August last, through the kindness of Mr. A. J. Hillis. 

The pitch of Scheibler’s forks being determined at about 
70° F., and the variation being about ‘00005 per vibration 


340 . Mr. D. J. Blaikley on the Correction to be added 


per degree, the pitch of those I used would be as follows at 
60° F.:—c' 253°68, e’ 317°46, g’ 380°81, 09’ 444-72, and ¢/ 
507°45. 
Table of observed lengths, in inches, from open end of 
tube to first node, reduced to 60° F. 


No. of ob- ' ! 1 ! W 
servation. Gi ee J: » . ahs 
ili: 12:568 9971 8176 6897 5974 
2. 12°618 9912 8:196 6877 5994. 
ay 12°588 9-961 8196 6°887 5-974 
4 12-608 9921 8-216 6897 5-994 
5. 12:598 9-961 8196 6°887 6:034 
6. 12-608 9-951 8206 6:897 6°024 
Whe 12°598 9971 8222 6:°897 6:004 
8. 12°608 9-981 8:192 6°893 6-024. 
9. 12°578 9-971 8°222 6913 6°044 
10. 12°632 9-971 8202 6:923 6:024 
ile 12:572 9:961 8:242 6893 5-974. 
12. 12°632 9°951 8:192 6910 6:024. 
ley 12-636 9951 8242 6'890 6:024. 
14. 127616 | 9-961 8232 6°920 5994. 
15. 12°620 9-961 8-222 6:880 6-014 
16. 12630 9-961 8212 6910 5974 
lve 12°600 9971 8222 6917 6014 
18. 12-610 9-951 8222 6-917 6014 
19. 12-620 9°961 8-242 6917 5-994 
20. 12-620 9-981 8222 6°917 6-014 
Average...| 12°608 9°959 8-214 6-902 6-006 


Table of observed lengths, in inches, from open end of 
tube to second node, reduced to 60° F. 


No. of ob- c e! g' ap! cl 
servation. c . ; ; : 


if 39013 31:162 25°831 21°849 19224 
2 39:033 31°152 25°831 21-909 19 204 
3 39023 31:142 25°871 21-899 19-194 
4. 38°993 31-172 25°83 1 21°859 19:214 
5. 39°025 31:201 25°861 21-929 19°224 
6 
7 
8 
9 


———y 


38°975 31181 25°87 1 21-919 19-234 
39°025 31162 25°920 21-959 19-224 
39°025 31:162 25-900 21-919 19°234 
39:°016 31-211 25°851 21:949 19°224 


10. 39:036 31181 25°831 21-949 19-244 
1 39-026 31:169 25°866 21°947 19-206 
12. 39038 31-189 25-886 21-957 19-206 
13. 39°028 31:169 25-906 21:937 19-236 
14. 39-038 31-179 25°856 21:977 19°246 
15. 38:°988 31:199 25°896 21-927 19216 
16. 39008 31°156 25°876 21-967 19-206 ° 
17. 39:060 31:176 25:°876 21-967 19-226 
18. 39°020 31-176 25°903 21-967 19-206 
19. 38-990 31:186 25°883 21:977 19:246 
20. 39°050 31°156 25°893 21:°957 19°226 


Average...| 39-020 31-174 - 25°872 21-936 19-222 


to the Length of a Cylindrical Resonant Tube. 341 


Let L=wave length ; 

/,=length from open end to first node ; 
ae S + second node ; 
x= correction for open end. 

Then L=2(l,—1,), and eG —h= 25h, 

The lengths as tabulated, however, require further slight 
corrections to obtain the true values of J, and J,. The dis- 
turbing influences are :— 

1. The slight veiling of the open end caused by the position 
of the fork (equivalent in effect to a certain increase in the 
length of the tube). 

2. The slight. variations in the pitch of the forks, due to 
changes of temperature. 

3. Capillary attraction. 

4. Humidity. : 

I found by experiment with two organ-pipes set slightly 
out of unison, and with plain open cylindrical tubes sounded 
by blasts across their ends, that a fork held over one of two 
such pipes caused an easily recognized difference in the num- 
ber of beats ; for the forks and tube I used, the value of this 
correction is about ‘0071 inch. 

For the second correction I take the variation in the pitch of 
the forks as being equal to-00005 per vibration per degree Fahr. 

The third possible disturbing influence I found was not mea- 
surable in a tube of the diameter used. 

The observations being taken on different days, the varying 
humidity of the air must be taken into account: I regret that I 
had no means of doing this at the time; but I have availed 
myself of the observations taken at the Royal Botanic Gardens 
(about a mile distant from the place where I worked) to form 
an estimate of the correction due to aqueous vapour. 

The dates of the observations, with the values of these differ- 
ent corrections to reduce the results to a standard for dry air at 
60° Fahr. are here given :— 


ae Average| Tension Corrections. Sum of 
ise Pitch. | tempe- CoS eon oer oni 
878. rature. | vapour. 1. 2. 4. ge re 
+ a a — 
fe) 
Sept. 23.| c’’ ) | 61-0 293 0071 | -0003| -0187 | -0119 
Beet | OS | agian 282 0071 | -0004 | -0206 | -0139 
es ges St Ges 260 O07. 0007") "0221 a Otag 
eG: | a! \z 63-0 ‘264 0071 | -0015 | -0275 | -0219 
etal chs) = a6a-7 294. ‘0071 | -0023 | -0388 | -0340 
Seon al Ne cal Gae2 -308 0071 | -0031 | -0612 | -0572 
Me egte rath «(GOs 362 ‘0071 | -0119 | -0994 | -1042 
» 8.2. $3]. 68-4 335 0071 | -0131 | -1197 | -1257 
oe T.| ce? rc] G24 308 ‘0071 | -0047 | -1256 | -1232 
ids) GD) aul 620. | “241 0071 | -0022 | -0557 | -0508 


542° Mat JD. ae Blaikley on the Correction to be added 


Rectifying the average of the tabulated observations by the 
value of the corrections above given, the following reduced re- 
sults are obtained for dry air at 60° F. 

ce". bb’. g' e! e! 

19-1648 21°8852 25°7678 31:0483 38°8968 


l, = 
I = 59941 68881 81983 9-9371 125740 
= = 131707 149971 175695 21-1112 263228 
= Sie ae aE RRR 2 
7 = 658583 74985 87848 105556 131614 
59941 68881 81983 9-9371  12°5740 
x= 5912 6104 “5865 6185 ‘5874. 
z= 568° ‘587 564. 59D 565 
2-08 
R= a = "| 
- 1:04 
Pitch. E Feet per 
: 2 second. R 
atts 507-45 X213:1707 = 1113-91 568 
bp’ ... 444-°72x2%14:9971 = 111159 +587 
@ bile 380°81 X217:5695 = 111511 564 
Bie ees 317-46 X2x21-:1112 = 1116-98 +595 


Ccte 253°68 X 2X 26:3228 = 1112-91 565 
Mean of all the obser- : LAUR 
vations at 60° ...... } ee oe 


Do. do. 382° 1088-75 


—__. 


The possible sources of error in the above results would appear 
to be chiefly these—inaccuracy in appreciation of the point 
of maximum resonance, and error in estimating the humidity 
of the air in the tube; perhaps vapour rising from the water 
surface would cause the air in the tube to be more nearly satu- 
rated than the surrounding air. ; 

x 


The differences in the values of Ry are very slight, and appear 


to be due rather to errors of observation than to any variation 
depending upon ratio of length to diameter, at least within the 
limits of an octave. 

The second method of experiment I adopted was to sound an 
open tube by means of a steady gentle blast across one end. 
The tube used was the same as used for the first method; and its 
second proper tone was sounded; so that two nodes would fall 
within its length: the pitch was 506°8. After the pitch was 
noted, a well-fitting sliding plug was inserted at the free end 
and moved along the tube until the two positions were found at 
which the note sounded agreed in pitch with that given by the 
open tube.. The nodes thus formed were at6:06 inches and 19°39 
inches from the free open end, with temperature 66° F’. and ten- 


to the Length of a Cylindrical Resonant Tube. 348 
sion of vapour ‘389 in. Reducing to dry air at 60°, ,= 6-000; 
oy = BEIRBE 2 =135:199; 2="6; and ='9717, 

(Pitch =506°8 x 2 x 13'199 in.=1114°88 ft. per second 

at 60°, or 108452 at 32°.) 

The velocity and value of rr thus found agree remarkably 
closely with the mean of all the observations by the first 
method. 

Regnault’s experiments give a mean limiting velocity at 
32° in a tube of 4°25 inches diameter, of 1071-74 feet; but pro- 
bably the pipe used by him had not so smooth an interior sur- 
face as the mandril-drawn tube used in my experiments ; 
this would doubtless cause a difference in the loss of velocity 
through skin-friction. | 

A third method of experiment I attempted to carry out, 
with, however, but rather uncertain results, for the purpose of © 
determining the velocity in smooth small tubes, such as are 
used in brass wind instruments. It is possible to sound notes 
with the lips on such cylindrical tubes without any bell-mouth; 
I used them in this manner, both for 1z and 27 wave-lengths. 
Any slight inaccuracy that may possibly be due to the lips not 
being exactly at a nodal point is eliminated by making use of 
the difference in length only between the tubes of 14 and 2} 
wave-lengths ; in this way the additional length of tube re- 
quired for 1 wave-length is obtained. The tubes used were 
surrounded by larger tubes; and the space between the two 
was filled with water to prevent the heating of the tubes by 
the breath. The notes were held for ten seconds at a time ; and 
between each trial air was fanned through to get rid as much 
as possible of the moist breath. In all, fifty observations were 
made with a tube of :434 in. diam., and twenty with a tube 
of 1:043 in. diam. The different observations with each tube 
did not agree so nearly as I had hoped ; but the mean results 
show a rapid decrease in velocity with decreasing diameter of 
tube, as will be seen from the following summary of all the 
experiments. 


Diameter Velocity in 

in inches. feet at 60°. 
"A 34 1092°3 
1:043 1110°5 
2:080 1114°1 


The velocities as above given are deduced from Scheibler’s 
standard of pitch as expiained. Konig’s standard, with which 
I have had an opportunity of comparing one of my forks du- 
ring the last few days, would give velocities about 2 feet legs. 


ee sae 


LIV. On the Dissipation of Energy. By Prof. P. G. Tarr. — 


To Sir W. Thomson, F.R.S. 


My prar THomson,— 

| ADDRESS you as one of the Editors of the Philoso- 

phical Magazine, but also specially as the first pro- 
pounder of the doctrine of the Dissipation of Energy. Ido 
so because Prof. Clausius, in the second part of the new 
edition of his work on Thermodynamics, has challenged your 
claim to the well-known expression for the amount of heat dis- 
sipated in a non-reversible cycle. J think that the time has 
come for you to speak out on the subject, soas, if possible, to 
prevent further unnecessary discussions. 

I shall endeavour, so far as I can, to keep to matters of 
scientific importance ; but I must introduce the subject by a 
reference to the comments made by Prof. Clausius upon a 
- somewhat slipshod passage (§ 178) of my little work on 
‘Thermodynamics.’ That passage refers to the integral 


dg 
sae? 
to which I believe Rankine first called attention, but which is 
essentially connected with your doctrine. 

I cannot altogether complain of Prof. Clausius’s comments, 
because I cannot account for my having called the above in- 
tegral (in the way in which I have employed it) a positive 
quantity, except by supposing that in the revision of the first 
proof of my book I had thoughtlessly changed the word 
“negative” to “‘ positive.” This might easily happen from 
my having used a novel term, “ practical value,” in a somewhat 
ambiguous manner, at one place confounding it with “ realized 
value.” That the whole section was meant to bear the con- 
struction forced on it by Prof. Clausius is, I think, sufficiently 
disproved by its opening sentence, not to speak of the fact that 
no one in this country has so interpreted it. 

But there is a graver matter involved than any such mere 
slips of the pen; for Prof. Clausius asserts that the method I 
employ (and which I certainly obtained from your paper of 
1852) is inapplicable to any but reversible cycles. This, I 
think, is equivalent to denying altogether your claims in the 
matter. I therefore quote the whole passage, correcting, 
however, the above-mentioned slip, and slightly extending the 
latter part to make my meaning perfectly clear. 

Ҥ 178. The real dynamical value of a quantity, dg, of 
“heat is Jdg, whatever be the temperature of the body which 


Prof, P. G. Tait on the Dissipation of Energy. 345 
“contains it. But the extreme practical value is only 


“where ¢ is the temperature of the body, and ¢ the lowest 
“available temperature. This value may be written im the 
“ form 


ade Ji “ 


“Hence, in any cyclical process whatever, if g, be the whole 
“heat taken in, and gp that given out, the practical value is 


d 
J(q- i) — Jn { “2° 


‘“ Now the realized value is 


J(G1—o) 
“by the first law; and if the cycle be reversible, this must be 


“equal to the extreme practical value. Hence, in this parti- 
“ cular case, 


dg _ 
| =. 


‘But in general this integral has a finite negative value, 
“ because in non-reversible cycles the realized value of the heat 
“is always less than 

J(%1—%) — Jeo, 
‘¢ which is the extreme practical value. 

“ Hence the amount of heat lost needlessly, 7. e. rejected in 
“‘ excess of what is necessarily rejected to the refrigerator for 
producing work, is 
dg 

< 
‘“‘ This is Thomson’s expression for the amount of heat dissipated 
‘during the cycle (Phil. Mag. and Proc. R. 8. E. 1852,‘ On a 
“ Universal Tendency in Nature to Dissipation of Energy’). 
“Ttis, of course, an immediate consequence of his important 
“ formula for the work of a perfect engine. 

“TIt is very desirable to have a word to express the availa- 
“bility for work of the heat in a given magazine; a term for 
“that possession, the waste of which is called dissipation. |” 

As I based the greater part of the last chapter of my work 


—to 


* On this formula Prof. Clausius remarks, “ Die Unrichtigkeit dieses 
“ Resultates lasst sich leicht aus dem blossen Anblicke der Formel 
‘‘erkennen ”! 


346 Prof. P. G. Tait on the Dissipation of Energy. 


on your papers, mainly because they appeared to me to he 
* greatly superior to all others on the subject in the three very 
important qualities of simplicity, conciseness, and freedom 
from hypothesis, | am anxious to know whether the above 
passage meets with your approval. 

From Prof. Clausius’s comments it appears, as I have 
already said, that he considers the method I have adopted 
from you to be one which cannot be applied except to re- 
versible cycles, and which, therefore, it is absurd to employ — 
in any argument connected with dissipation of energy. 

Prof. Clausius also disputes the correctness of my reference 
to your paper in the Philosophical Magazine, as containing 
the above expression for the heat dissipated. You ought to 
be a competent authority on such a question as this. 

I do not now reply to the many other remarks of Prof. 
Clausius, simply because they refer to myself, my motives, 
and my book, and not to the principles or the history of 
science. Ag the matter affects you, however, I may mention 
that Professor Clausius attributes to me the real authorship of 
the paper on “ Energy”? which we jointly wrote for ‘ Good 
Words,’ and which has been often referred to in the Philoso- 
phical Magazine. 

But the passage in brackets in the extract above indicates a 
want of proper nomenclature, which would, I think, be well 
met by the publication of the paper on Thermodynamic Mo- 
tivity, read by you some years ago to the Royal Society of 
Edinburgh. 

Yours truly, 


38 George Square, Edinburgh, Pp, Go ear: 
March 17th, 1879. 


Note by Sir W. Thomson on the preceding Letter. 


The passage quoted, with amendments, by Professor Tait 
from his ‘ Thermodynamics,’ seems to me perfectly clear and 
accurate. Taken in connexion with the sections which pre- 
ceded it in the original, its meaning was unmistakable; and. 
a careful reader could have found little or no difficulty in 
making for himself the necessary corrections with which Pro- 
fessor Tait now presents it. It is certainly not confined to 
reversible cycles; but, on the contrary, it gives an explicit 
expression for the amount of energy dissipated, or, as I put it, 
‘absolutely and irrecoverably wasted” in operations of an 
irreversible character. My original article ‘‘ On a Universal 
Tendency in Nature to the Dissipation of Mechanical Energy,” 


Sir W. Thomson on the Dissipation of Energy. 347 


communicated to the Royal Society of Edinburgh in April 
1852, and published in the ‘ Proceedings’ of the Society for 
that date, and republished in the Philosophical Magazine for 
1852, second half year, is a sufficient answer to the challenge 
referred to in the opening sentence of Professor Tait’s letter. 

I think Professor Tait quite right in referring also to that . 


paper for the formula ¢) a7. The whole matter is contained 
1(S 

in the formula we- aM ui which is given explicitly in that 

paper. At the top of the next page in the Philosophical Ma- 

gazine reprint the following passage occurs:—“ If the system 


of thermometry adopted be such that w= = that is, if we 
agree to call :- a the temperature of a body, for which p is, 


the value of Carnot’s function (« and J being constants), &e.;” 
and on the word “adopted” the following footnote is given : 
“ According to Mayer’s ‘hypothesis’ this system coincides 
“ with that in which equal differences of temperature are defined 
‘fas those with which the same mass of air under constant 
“pressure has equal differences of volume, provided J be the 


** mechanical equivalent of the thermal unit, and : the coeffi- 


“ cient of expansion of air.”’ Here the true foundation of the 
absolute thermodynamic scale now universally adopted was, I 
believe, for the first time given. — I had previously, in Part III. 
of my “ Dynamical Theory of Heat,” published in the Transac- 


. tions of the Royal Society of Edinburgh, and in the Philoso- 


phical Magazine for 1852, second half-year, taking advantage 
of a suggestion made to me by Joule, in a letter of date De- 
cember 9, 1848, shown that the assumption p= reduces 
1 (’S 
the formula wen 3 Jr ’ to wete and I used this transforma- 
tion in the concluding formulas of the article referred to by 
Professor Tait (corrected in the errata of Phil. Mag. 1853, 
first half-year). It was not, however, until the experiments 
by Joule and myself, made in the course of the years 1852, 
1853, and the early part of 1854, on the thermal effects of 
forcing air and other gases through porous plugs, had proved 
that my proposed thermodynamic scale agreed as nearly with 
the scale of an air-thermometer as different air-thermometers 
agreed with one another, that I definitively adopted it in fun- 
damental formulas of thermodynamics. Thus, for example, 
in Part VI. (“Thermo-electric Currents’) of my “ Dynamical 


348 Sir W. Thomson on Thermodynamic Motivity. 


Theory of Heat,” published in the Transactions of the Royal 
Society of Hdinburgh for May 1854, and in the Philosophical 
Magazine for 1855, first half-year, the formula . 


mM ay Fer ye 


pote totaal 


Is given as an equivalent for 


1 (t 
Sa, Sasser na) 

which was first published in the Proceedings of the Royal 
Society of Edinburgh for 1851, and Phil. Mag. 1852, first 
half-year. Tait had actually quoted the formula from my 
1854 paper in § 176 of his book, and so left absolutely no 
foundation for Professor Clausius’ objection to his saying 
“ This is Thomson’s expression &c.,’’ quoted in his letter above. 

As to the ‘Good Words’ article on Energy which appeared 
under our joint names, Professor Tait and I are equally 
responsible for its contents. I claim my full share of the 
“scientific patriotism ’’ commended in that article, and cannot 
assent to Professor Clausius’ giving all the credit of it to Pro- 
fessor Tait. : 

In compliance with the concluding sentence of Professor 
Tait’s letter, I hope in the course of a few days to write out, 
‘and send tothe Philosophical Magazine for publication, a short 
statement of the communication on Thermodynamic Motivity 
which I made vivd voce to the Royal Society of Edinburgh on 
April 3rd, 1876. 


LV. On Thermodynamic Motiwity. 
By Sir W. THomson, P.2.S.* 


(Aue having for some years felt with Professor Tait the 

want of a word “to express the Availability for work 
“ of the heat in a given magazine, a term for that possession 
“ the waste of which is called Dissipation’’}, I suggested three 
years ago the word Motivity to supply this want, and made a 
verbal communication to the Royal Society of Edinburgh de- 
fining and illustrating the application of the word ; but as the 
communication was not given in writing, only the title of the 
paper, “ Thermodynamic Motivity,” was published. In con- 
sequence of Professor Tait’s letter to me, published in the 
present Number of the Philosophical Magazine, I now offer, 


* Communicated by the Author. 
+ Tait’s ‘Thermodynamics,’ first edition (1868), § 178: quoted also 
in Professor Tait’s letter in the present Number of the Philosophical 


Magazine, 


Sir W. Thomson on Thermodynamic Motivity. 349 


for publication in the Proceedings of the Royal Society of 
Edinburgh and in the Philosophical Magazine, the following 
short. abstract of the substance of that communication. 

In my paper on the Restoration of Energy from an Un- 
equally Heated Space, published in the Philosophical Maga- 
zine in January 1853, 1 gave the following expression for the 
amount of “mechanical energy” derivable from a body, B, 
given with its different parts at different temperatures, by the 
equalization of the temperature throughout to one common 
temperature* 'T, by means of perfect thermodynamic engines, 


Wad { { i} dady dz oat 1—e"3Sy"), git os) 


where ¢ denotes the temperature of any point x, y, z of the 
body, c the thermal capacity of the body’s substance at that 
point and that temperature, J Joule’s equivalent, and mu 
Carnot’s function of the temperature ¢. 


Further on in the same paper a simplification is introduced 
thus :— 3 


“ Let the temperature of the body be measured according to 
‘‘ an absolute scale, founded on the values of Carnot’s function, 
‘and expressed by the following equation, 


J 


t=-—a4, 


be 


“ where # is a constant which may have any value, but ought 
“ to haye for its value the reciprocal of the expansibility of air, 


* In the present article I suppose this temperature to be the given tem- 
perature of the medium in which Bis placed; and thermodynamic engines 
to work with their recipient and rejectant organs respectively in connexion 
with some part of B at temperature ¢, and the endless surrounding matter 
at temperature T. In the original paper this supposition is introduced 
subordinately at the conclusion. The chief purpose of the paper was the 
solution of a more difficult problem, that of finding the value of T,—a 
kind of average temperature of B to fulfil the condition that the quantities 
of heat rejected and taken in by organs of the thermodynamic engines at 
temperature T are equal. The burden of the problem was the evaluation 
of this thermodynamic average ; and I failed to remark that when the 
value which the solution gave for T is substituted in the formula of the 


text it reduces to J NK) dx dy da \ 7. edt, which was not instantly obvious 


from the analytical form of my solution, but which we immediately see 
must be the case by thinking of the physical meaning of the result; for the 
sum of the excesses of the heats taken in above those rejected by all the 
engines must, by the first law of thermodynamics, be equal to the work 
gained by the supposed process. This important simplification was first 
given by Professor Tait in his ‘Thermodynamics’ (first and second edi- 
tions). It does not, however, affect the subordinate problem of the original 
paper, which is the main problem of this one. 


Phil. Mag. 8. 5. Vol. 7. No. 44. May 1879. 2K 


350 Sir W. Thomson on Thermodynamic Motivity. 


“in order that the system of measuring temperature here 
“‘ adopted may agree approximately with that of the air-ther- 
‘‘mometer. Then we have | 
Se Nude Ee 
| ae =7y! +e 
It was only to obtain agreement with the zero of the ordi- 
nary Centigrade scale of the air-thermometer that the a was 
needed ; and in the joint paper by Joule and myself, published 
in the Transactions of the Royal Society (London) for June 
1854, we agreed to drop it, and to define temperature simply 
as the reciprocal of Carnot’s function, with a constant coeffi- 
cient proper to the unit or degree of temperature adopted. © 
Thus definitively, in equation (6) of § 5 of that paper, we took 


t= -—, and have used this expression ever since as the expres- 


sion for temperature on the arbitrarily assumed thermody- 
namic scale. With it we have 


IGe 
; ele = a 4) ge a aa 
and by substitution (1) becomes 


? if 
W=J ladydz\ cdt{1——). .. €4 
S\Jaedae{ (1-7) 


Suppose now B to be surrounded by other matter all at a 
common temperature T. The work obtainable from the given 
distribution of temperature in B by means of perfect thermo- 
dynamic engines is expressed by the formula (4). If, then, 
there be no circumstances connected with the gravity, or elas- 
ticity, or capillary attraction, or electricity, or magnetism of 
B in virtue of which work can be obtained, that expressed by 
(4) is what I propose to call the whole Motivity of B in its 
actual circumstances. If, on the other hand, work is obtain- 
able from B in virtue of some of these other causes, and if V 
denote its whole amount, then 


ii—=V+tW... « 2 (5) 


is what I call the whole Motivity of B in its actual circum- 
stances according to this more comprehensive supposition. 
We may imagine the whole Motivity of B developed in an 
infinite variety of ways. The one which is obvious from the 
formula (5) is first to keep every part of B unmoved, and to 
take all the work producible by perfect thermodynamic en- 
gines equalizing its temperature to T; and then keeping it 
rigorously at this temperature, to take all the work that can 


Sir W. Thomson on Thermodynamic Motivity. 851 


be got from it elastically, cohesively, electrically, magnetically, 
and gravitationally, by letting it come to rest unstressed, dis- 
electrified, demagnetized, and in the lowest position to which 
it can descend. But instead of proceeding in this one defi- 
nite way, any order of procedure whatever leading to the 
same final condition may be followed ; and, provided nothing 
is done which cannot be undone (that is to say, in the tech- 
nical language of thermodynamics, provided all the operations 
be reversible), the same whole quantity of work will be ob- 
tained in passing from the same initial condition to the same 
final condition, whatever may have been the order of pro- 
cedure. Hence the Motivity is a function of the temperature, 
volume, figure, and proper independent variables for express- 
ing the cohesive, the electric, and the magnetic condition of 
B, with the gravitational potential of B simply added (which, 
when the force of gravity is sensibly constant and in parallel 
lines, will be simply the product of the gravity of B into the 
height of its centre of gravity above its lowest position). So 
also is the Hnergy of a body B (as I first pointed out, for the 
case of B a fluid, in Part V. of my Dynamical Theory of 
Heat, in the Transactions of the Royal Society of Edinburgh 
for December 15, 1851, entitled, “On the Quantities of Me- 
chanical Energy contained in a Fluid in Different States as 
to Temperature and Density’’). Consideration of the Knergy 
and the Motivity, as two functions of all the independent vari- 
ables specifying the condition of B completely in respect to 
temperature, elasticity, capillary attraction, electricity, and 
magnetism, leads in the simplest and most direct way to 
demonstrations of the theorems regarding the thermodynamic 
properties of matter which I gave in Part III. of the Dynamical 
Theory of Heat (March 1851); in “Part VI. of Dynamical 
Theory, Thermoelectric Currents,” (May 1, 1854); in a paper 
in the Proceedings for 1858 of the Royal Society of London, 
entitled, ““On the Thermal Effect of Drawing out a Film of 
Liquid ;”’ and in a communication to the Royal Society of 
Hdinburgh (Proc. R. 8. H. 1869-70), “ On the Equilibrium 
of Vapour ‘at the Curved Surface of a Liquid;” and in my 
article on the Thermoelastic and Thermomagnetic Properties 
of Matter, in the first number of the Quarterly Journal of 
Mathematics (April 1855); and in short articles in Nichol’s 
Cyclopedia, under the titles ‘Thermomagnetism, Thermo- 
electricity, and Pyroelectricity,’ put together and repub- 
lished with additions in the Philosophical Magazine for Ja- 
nuary 1878, under the title “ On the Thermoelastic, Thermo- 
magnetic, and Pyroelectric Properties of Matter.” 

It would be beyond the scope of the present article to enter 

2H 2 


352 Dr. C. W. Siemens on the Transmission and 


in detail into these applications, which were merely indicated 


in my communication to the Royal Society of Hdinburgh of 
three years ago, as a very short and simple analytical method 
of setting forth the whole non-molecular theory of Thermo- 
dynamics. 


. University of Glasgow, 
April 11, 1879. 


LVI. On the Transmission and Distribution of Energy by 
_ the Electric Current. By C. WitutAm Siemens, D.C.L., 
Be IS. 
[Plate XIL.] 


rE the autumn of 1876, when standing below the Falls 
of Niagara, the first impression of wonderment at the 
imposing spectacle before my eyes was followed by a desire 
to appreciate the amount of force thus eternally spent with- 
out producing any other result than to raise the temperature 
of the St. Lawrence a fraction of a degree{, by the concus- 
sion of the water against the rocks upon which it falls. ) 

The rapids below the fall present a favourable opportunity 
of gauging the sectional area and the velocity of the river; 
and from these data I calculated that the fall represents energy 
equivalent to nearly 17 million horse-power, to produce which 
by steam would require about 260 million tons of coal a year, 
- or just about the entire amount of coal raised throughout the 
world. 

If one fall represents such a loss of power, what must be 
the aggregate loss throughout the world from similar causes ? 
and is it consistent with utilitarian principles that such stores 
of energy should go almost entirely to waste? But the diffi- 
culty arises, how such energy (occurring as it does for the 
most part in mountainous countries) is to be conducted to 
centres of industry and population. 

Transmission by hydraulic arrangements or by compressed 
air would be very costly and wasteful for great distances ; 
but it occurred to me that large amounts of energy, produced 
by means of the dynamo-electric current-generator, might be 
conveyed through a metallic conductor, such as a rod of 
copper fixed upon insulating supports. Such a conductor 
would no doubt be expensive ; but, if once established, the 
cost of maintenance would be very small, and its power of 

* Communicated by the Physical Society, haying been read at the 
meeting on February 22. : 


t+ The vertical fall being 150 feet, the increase of temperature would he 
4159 =1° Wahrenheit nearly. 


Lc 


Distribution of Energy by the Electric Current. 353 


_ transmitting electric energy would be limited only by the 


heat generated 1 in it through electric resistance. 

In venturing to give expression to my thoughts upon this 
subject, in my address to the Iron and Steel Institute in March 
1877, I stated that a copper rod 3 inches in diameter would 
be capable of transmitting energy to the extent of a thousand 
horse-power an hour a distance of 30 miles, there to give 
motion to electrodynamic engines, or to produce illumination 
sufficient to light up a town with 250,000 candle-power. 

Although this statement was considered by many a bold 
one at the time it was made, I now find that a conductor 
such as I then described might be able to transmit three or 
four times the amount of power then named, and that the 
light producible per horse-power was also, according to our 
present more advanced state of knowledge, very much under- 
stated. 

No serious difficulty need be apprehended as to the pro- 
duction of a current sufficient in amount to fill a conductor 
of such large proportions as here indicated. Although it 
would perhaps be impossible to construct a single dynamo- 
electric machine of sufficient power for that purpose, any 
number of smaller machines could be easily coupled up both 
for intensity and quantity to produce the desired aggregate 
amount. 

A difficulty would, however, arise at the other end, where 
the electric energy was to be applied, and where it would 
therefore be requisite to have an arrangement for its distri- 
bution over a number of branch circuits, so that each might 
receive such a proportion of the total current in the main 
conductor as to produce the number of lights, or the amount 
of power intended to be supplied. An accidental increase 
of resistance in one or other of the branch circuits would 
produce the double inconvenience of starving the circuits in 
which such increased resistance had occurred and of supply- 
ing an excess of current to the other circuits. 

In order to carry out such a system of supply, it would be 
necessary to have the means of so regulating the current in 
each branch circuit, that only a predetermined amount should 
be allowed to flow through the same; it would be desirable 
also to furnish each circuit with the means of measuring and 
recording the amount of electric current passed inoue the 
same in any period of time. 

It is my special purpose to bring before you an fe errane 
by which these two purposes can be accomplished. The 
current-regulator (as represented in Plate XII.) consists 
principally of a strip of metal (of mild steel or fused iron by 


354. Dr. C. W. Siemens on the Transmission and 


preference), which by its expansion and contraction regulates 
the current passing through it. This strip is rolled down to 
a thickness not exceeding 0:05 millim., and is of such a 
breadth that the current intended to be passed through the 
regulated branch circuit would raise the temperature of the 
strip to say 50° C. 

This strip of metal (A) is stretched horizontally between a 
fixed support and a regulating-screw (B), at which latter the 
current enters, passing through the strip, and thence through 
a coil of German-silver wire (C) laid in the form of a collar 
round the centre, and connected at its other extremity with a 
binding-screw (D), whence the current flows on towards the 
lights or other apparatus to be worked by electricity. Upon 
its middle the strip carries a saddle of insulating material, 
such as ebonite, upon which rests a vertical spindle, support- 
ing a circular metallic disk (H), with platinum contacts 
arranged on its upper surface. Ten or any other number of 
short stout wires connect the helical rheostat at equidistant 
points with adjustable contact-screws (I), standing above the 
platinum contacts on the surface of the metallic disk. ‘These 
wires are supported upon the circular frame (G) of wood or 
other insulating material, but are free to be lifted off their 
support if the metallic disk should rise sufficiently to be brought 
into contact with the screws. These latter are so adjusted 
that none of them touches the metallic disk when it is«in its 
lowest position, but that they are brought one after another 
into contact with the same as the disk rises; and it will be 
easily seen that for every additional contact-screw that is 
raised seriatim by the disk, a section of the helical rheostat 
between attachment and attachment is short-circuited by the 
metallic disk, and thus excluded from the circuit. When the 
disk is in its uppermost position the whole of the rheostat is 
short-circuited, and the regulator offers no other resistance to 
the current than that of the horizontal strip itself. In setting 
the regulator to work the regulating-screw (B) is drawn on 
sufficiently to bring the whole of the contact-screws into con- 
tact with the disk. The passage of the current through the 
strip will have the effect of raising its temperature to an ex- 
- tent commensurate with the electrical resistance; and in the 
same measure the strip itself will be elongated, and cause the 
spindle with the contact-disk to descend. 

Another form of this instrument depends for its action 
upon the circumstance discovered by the Count du Moncel in 
1856, and more recently taken advantage of by Mr. Hdison, 
that the electrical resistance of carbon varies inversely with 
the pressure to which it is subjected. A steel wire of 0°3 


Distribution of Energy by the Electric Current. 355 


millim. diameter is attached at one end to an adjusting- 
screw, B, and at the other to one end of a bell-crank lever, 
Li, by means of which the pressure is brought to bear upon a 
pile of carbon disks, C, placed in a vertical glass tube. The 
current enters the instrument at the adjusting-screw B, and, | 
passing through the wire and bell-crank lever, leaves below 
the pile of carbon disks. Its effect is to cause a rise of tem- 
perature in the steel wire, which, through its expansion, 
diminishes the pressure upon the carbon disks, and thus pro- 
duces an increase in their electrical resistance. This simple 
apparatus thus supplies a means of regulating the strength 
of small currents, so as to vary only within certain narrow 
limits. 

According to Joule’s law the heat generated in the strip 
per unit of time depends upon its resistance, and upon the 
square of the current ; or 


H 
H=O(°R, ... C= / = 


On the other hand, the dissipation of heat by radiation de- 
pends upon the surface of the strip, and upon the difference 
between its temperature and that of the.air. Therefore, in 
order that the current C may remain constant, it must, at 
every moment, be equal to the square root of the tempera- 
ture divided by the resistance ; and this function is performed 
automatically by the regulator, which throws in or takes out 
resistance in the manner described, according as the tempe- 
rature increases or diminishes. 

The regulating instrument may also be adapted to the 
measurement of powerful electric currents, by attaching to 
the end of the sensitive strip a lever, with a pencil pressing 
with its point upon a strip of paper drawn under it in a 
parallel direction with the lever by means of clockwork, a 
datum line being drawn on the strip by another pencil. The 
length of the ordinate between the two lines depends, in the 
first place, upon the current which passes at each moment, 
and, in the second place, upon the loss of heat by radiation 
from the strip. 

If R’is the resistance and H’ the heat with a current C’ 
and temperature T’, then, by the law of Joule, 


4 ia bf sey ice 
and the loss by radiation is equal to 
H’=(T’—T)S, 
in which T’ is the temperature of the strip, T that of the at- 
mosphere, and § the surface of the strip. 


356. Messrs. Wanklyn and Cooper on the 


Considering that the resistance varies as the absolute tem- 
perature of the conductor, according to a law first expressed 
by Helmholtz, the value of BR may be put for R’ for small 
variations of temperature ; ; and as during an interval of con- 
stant current the heat generated and that radiated off will be 
equal, we obtain 


C#=(V Te “. c=) is a) 


in which T!—T represents the movement of the pencil, and § 
is constant. 
_ For any other temperature T", 


je LS 
Oma] aR ny 


For small differences of C” and C', 

(C"—C'!)?=20"(C"—0) ; 
that is to say, small variations of current will be proportional 
to the variations in the temperature of the strip. © 

To determine the value of a diagram in Weber’s or other 
units of current, it is only necessary, if the variations are not 
excessive, to average the ordinates, and to determine their 
value by equation (1), or from a Table. 

These observations may- suffice to show the possibility of 
regulating and measuring electric currents with an ease and 
certainty quite equal to that obtained in dealing with currents 
of liquids such as gas or water; and the time may not be far 
distant when the use of such an instrument will also become 
a public necessity. 

Other forms of the instrument will readily suggest them: 
selves to the mind of the constructive engineer; but the two 
typical forms I have described on this occasion will suffice, 
I think, to show its general character. 


LVII. Products of the Oxidation of Wool. Cyano-propionic* 
Acid. By J. ALFRED WANKLYN and W. J. CooPER fj. 


N the course of the investigations which have led up to 
the moist-combustion process, we have come across some 
results which appear to be worth recording. On the present 
oceasion we single out the oxidation of wool, so as to produce 
large quantities ‘of a new nitr ogenous acid endowed with great 
stability. 
When wool, dissolyed in water by the aid of about three 
* Apparently, judging from the reaction with potash, the acid is iso- 


cyano-propionic acid.—J. A. W. 
+ Communicated by the Authors. 


Products of the Oxidation of Wool. oat 


times its weight of caustic potash, is oxidized by four times 
its weight of permanganate of potash, there are produced car- 


-bonie acid, oxalic acid, and a certain quantity of ammonia ; 


and when the oxidation is limited by the employment of only 
four times as much permanganate as wool, at least two new 
acids survive, one of which (viz. cyano-propionic acid) we 
have succeeded in obtaining in a state of purity. 

The acids arising from oxidation under these conditions are 


--met with in combination with potash, and mixed with the 


excess. of caustic potash and the carbonate and oxalate of 
potash arising from the oxidation of the wool. The alkaline 
liquid is first filtered from the brown oxide of manganese 
resulting from the destruction of the permanganate ; and then 
it is neutralized with sulphuric acid, and evaporated down to 
erystallization. After the deposit of the greater part of the 
sulphate of potash, the mother-liquor contains oxalate of 
potash, which may be precipitated by the addition of weak 
alcohol ; and after the separation of the oxalate of potash, the 
alcoholic mother-liquor will be found to contain the potash- 
salts of at least two new organic acids. One of these new 
salts is very soluble in weak alcohol of 40 or 50 per cent., but 
almost. insoluble in alcohol of 84 per cent.; and this salt, 
which is cyano-propionate of potash, we have investigated. 
In our first attempts we endeavoured to take advantage of 
this character in order to purify the salt; but we afterwards 
found that the baryta-salt admits of a most satisfactory mode 
of treatment, and have accordingly resorted to the baryta-salt. 
We proceed to describe our experiment:—A large Berlin 
porcelain dish, capacity from 5 to 6 litres, was fitted into a 
water-bath and heated to 100° C. One litre of water, 800 grms. 
of solid potash, and 100 grms. of Berlin wool were next placed 
in the dish, and heated and stirred until the wool had com- 
pletely dissolved in the alkaline liquid. That having been 
done, another litre of water was added, and 400 grms. of 
erystals of permanganate of potash were carefully and gradually 
dropped into the alkaline liquid. The action was energetic : 
ammonia was evolved; brown hydrated binoxide of manganese 
was precipitated; and in a short time the colour of the perman- 
ganate had completely disappeared. The whole was then 


- allowed to settle, and partly by decantation and partly by fil- 


tration the alkaline liquid was separated from the brown oxide 
of manganese. : 

The alkaline liquid was nearly neutralized with sulphuric 
acid, and evaporated until crops of sulphate of potash separated. 
Care was taken to wash each crop of sulphate of potash with 
repeated small quantities of water, so as to avoid loss of soluble 


308 Messrs. Wanklyn and Cooper on the 


product; and the mother-liquor was mixed with a little alcohol, 
which threw down a quantity of oxalate of potash. Finally 
about 500 cub. centims. of solution, containing the new salts 
dissolved in alcohol of 50 to 60 per cent., was obtained. This 
solution was evaporated down to a syrup ; and at this stage 
the exchange of barium for potassium was managed as 
follows:—To the syrup 20 grms. of H,OSOs3, previously 
diluted with about an equal volume of water, was added, so as 
to decompose the potash-salt. The resulting sulphate of potash. 
was separated from the new acid by means of 500 cub. centims. 
of 84-per-cent alcohol, which dissolved the new acid and left 
behind the sulphate of potash. The alcoholic solution was 
mixed with 30 grms. of baryta which had been slaked, a little 
more baryta being added so as to render the liquid alkaline. 
The alcohol was evaporated off, and the resulting baryta-salt 
dried up in the water-bath. After this evaporation to dryness, 
the baryta-salt was redissolved in water, and the solution fil- 
tered and mixed with its own volume of 84-per-cent. alcohol. 
By this treatment a white powdery precipitate of baryta-salt 
was obtained. The precipitate was washed with 40-per-cent. 
alcohol, and afterwards pressed for some days between folds 
of bibulous paper. . 4 

The weight of the pressed baryta-salt, which retained 
alcohol and water, was 85 grms., containing 25:1 grms. of 
baryta-salt absolutely dry at 100° C. 

One of the objects of this precipitation by means of an equal 
volume of 84-per-cent. alcohol (which is equivalent to the use 
of 40 per cent. alcohol) is the removal of a new baryta-salt 
which is very soluble in alcohol. 

The 85 grms. of pressed baryta-salt, containing 25°1 grms. 
of baryta-salt, formula (C, H, NBaO,)., 3H, O, are the mate- 
rial from which we have prepared the acid and the set of salts 
about to be described. 

In addition to the 25:1 grms. of baryta-salt, there were 
4 orms. of baryta-salt in the alcohol employed for washing the 
precipitate. The yield of cyano-propionate of baryta by 100 
erms. of wool was therefore 29°1 grms.; and, as will be seen 
on turning to the analysis, the carbon contained by the salt is 
2 orms. 

The Berlin wool employed in these experiments had been . 
previously examined; and a combustion of it had been made in 
the ordinary hygrometric condition in which it was employed. 
100 grms. of the wool contain 43°40 grms. of carbon. 

We have likewise made quantitative determinations of the 
carbonic acid and the oxalic acid given by the action of four 
parts of permanganate of potash on one part of wool dissolved 


Products of the Oxidation of Wool. 309 


in potash; also we have determined the oxygen consumed 
in the oxidation. The details of the experiments we will 
publish shortly ; and likewise we reserve our commentary on 
the bearing of these results on our views as to the structure of 
horn and albumen. 

Here we give the numerical results :— 

100 grms. of wool (containing 43:4 grms. of carbon), when 
submitted to oxidation by means of four times its weight of 
permanganate of potash, acting at 100° C. in alkaline solution, 
gave :— 


Garhon in the tom of CO): sas sacs5 ov atsesdie 5:9 grms 
é . Cpl Ol) | ocaek Saree 12:2.) 55 
ts ; ls WiOs eons bee (ig ery 

Carbon in other forms (mostly as forming 

acids with potash-salts very soluble in 
SURI AMMO) Basen cscissm canaries scish onsen ds 1B og 
43°4 orms. 


Oxygen consumed, 60°7 grms. 

Cyano-propionic Acid, (C,H; NOz)2, 8H, O.—This acid is 
prepared by decomposing the baryta-salt with the theoretical 
quantity of dilute sulphuric acid necessary to saturate the 
barium, separating the sulphate of baryta by filtration, and 
evaporating the solution of the acid to dryness in the water- 
bath. The solid residue, which was carefully dried in the 
water-bath, has the following formula— 

(Cy ia NO,)., 3 HS O. 

We took 16:0 grms. of the moderately but not excessively 
dry baryta-salt (the purity of which had been ascertained by 
a complete analysis of the sample), added 75:0 cub. centims. 
of normal sulphuric acid (3°675 grms. of H,OSOs;), and ob- 
tained 8°773 grms. of washed and ignited Baz OSO3, and 9:7 
grms. of the organic acid dried in a platinum dish at 100° C. 

The equation expressing the reaction is 

(Cy 7; BaNO,)s, 3 H, O EE EL OSO; 
= Bay OSO; a (Cy i. NOz)s, 3H, O 3 
and the following is a comparison between the quantities 
required by the equation and those given by experiment :— 
Theory. Experiment. 


orms. orms. 

(C, H, BaNO,),,3H,O os... 1451 160 
FOSO, 41 'S5:675 3-675 
Ba; OSOs 6) 8737 8-773 

(Cp HANDY SHE O ec. 9°45 9°7 


The correspondence between the sulphuric acid, sulphate of 


360. Messrs. Wanklyn and Cooper on the 


baryta, and final organic acid will be noted. The want 
of accordance between the quantity of baryta-salt taken and 
the quantity required by the equation, as will be understood, 
means that the salt was not in a state of absolute dryness. 
The correctness of this interpretation was borne out by the 
observation that on ignition the acid left no -appreciable fixed 
residue, viz. 0°774 grm. of the solid acid left, on careful 
ignition, 0-002 orm. of ash. The acid was also ascertained to 
be free from sulphuric acid. 

Properties of Cyano-propionic Acid.—It is an amorphous 
solid, brittle at ordinary temperatures, but easily softening on 
being heated to 100° C. Its colour is pale brownish yellow, 
or straw-colour ; in powder it is almost white. 

It is very soluble in water and in strong alcohol. Its 
aqueous solution is powerfully acid, both to the taste and to 
litmus. It drives out carbonic acid from carbonates, and neu- 
tralizes bases completely. 

The specific gravity of an aqueous solution of the acid con- 
taining 15-12 per cent. of (C,H;NO.)., 3H,O, is 1:06 at ordi- 
nary temperatures. An aqueous solution of one tenth of this 
strength, viz. containing 1°512 per cent., forms a lather on 
being shaken up, is pleasantly acid to the taste, and is capable 
of dissolving metallic magnesium in the cold. In presence of 
metallic mercury the action of the magnesium is brisk; and in — 
the space of twenty-four hours ten cubic centimetres of the 
weak acid liquid confined over mercury had evolved almost 
the theoretical quantity of hydrogen which the magnesium 
was capable of displacing. 

Cyano-propionic acid is attacked when it is sealed up in a 
tube with the acid 8-per-cent. bichromate solution and heated 
to 100° C. Under these conditions very little oxygen is taken 
up and carbonic acid is formed in considerable quantities. 

In alkaline solution, when boiled with permanganate of 
potash, it is slowly attacked, and takes up one third of its 
weight of oxygen. When heated to about 200° C. with great 
excess of potash, it suffers a very interesting decomposition, 
which we are at present investigating. ) 

When the acid is heated above 100° C. it loses weight, and 
becomes constant at about 140° C. After repeated heating to 
that temperature, the formula of the acid (judging by the loss 
of weight) appears to be C,H;NO,. At temperatures above 
140° C. the acid continues to lose in weight, but apparently 
undergoes decomposition, inasmuch as it evolves a very pecu- 
liar smell, reminding us of cyanide of ethyl. A portion of the 
acid which had been dried at 140° C. lost about half of its 
weight when heated to 220°C., and yielded a brown or black 


| 
| 
| 


Products of the Oxidation of Wool. 361 


mass insoluble in ether and water, but soluble in caustic 
potash. On ignition a small quantity of charcoal difficult of 
combustion remains. The proportion of such charcoal yielded 
by the acid dry at 140° C. is about one sixth of the weight of 
the acid. On continuing the application of heat this charcoal 
gradually burns away and no residue is left. 

As will be seen presently, most of the salts of cyano-pro- 
pionic acid are soluble in water, the only exceptions we have 
met with being the salts of silver, lead, and peroxide of iron. 
Solutions of cyano-propionates give no precipitate with salts 
of alumina, copper, and peroxide of mercury. Those cyano- 
propionates which are soluble in water are insoluble or very 
sparingly soluble in strong alcohol. Certain salts, as, for 
instance, those of lime, baryta, and magnesia, are very 
sparingly soluble even in 40-per-cent. alcohol. 

As a rule, the salts of this acid exist in combination with 
water. The only salt which we have found to be nearly an- 
hydrous is the silver salt. So far as we have ascertained, de- 
composition sets in before the hydrated salts give up the last 
portions of water. 

Cyano-propionate of Baryta, (CyH,N BaQO,), 3 H, O, is ob- 
tained in a state of purity, as has already been described, by 
precipitating its strong aqueous solution by means of an equal 
volume of 84-per-cent. alcohol. _ The precipitate is a powder 
almost absolutely white, which may be washed with 40-per- 
cent. alcohol, in which it is very sparingly soluble. It 
should be afterwards pressed between folds of bibulous paper 
and dried in the water-bath. After prolonged drying at 
100° C. it has the above formula, and has furnished the fol- 
lowing results on analysis :— 

I. 0°923 grm., burnt with chromate of lead, copper-turnings 
being used in front of the combustion-tube, gave 0°290 grm. 
of water and 0°842 orm. of carbonic acid. 

I]. 1-471 grm. gave 0°907 grm. of sulphate of baryta. 

ITI. 0°259 grm. gave 0°157 grm. of sulphate of baryta. 

IV. 0:958 grm. gave 0°587 grm. of sulphate of baryta. 

V. 0°398 grm., burnt with CuO and copper-turnings, gave 
20°61 cubic centims. of nitrogen gas at 0° C. and 760 mil- 
lims. N per cent. =6°51. 


(Cr. N BaO),) 5, oe Pond 
Calculated. oo  — 
—— Ter beter, SEER IV. V. 
Caressa 96 24-81 24-88 -— an es es 
i veee sere tlt 3°62 3°49 — — = nie 
shee ec 0) 7°23 _— hes. ee it 651 
Be A orice terre 35°40 — 36°26 35°64 36:03 US 
ect Ll 28:94 — ee ae salle 


587 100-00 


362 Messrs. Wanklyn and Cooper on the 


At 160° C. to 170° C. the salt loses one atom of water, be- 
coming (C,H, Ba NO,). 2H, O, but regains the water on ex- 
posure to the atmosphere at ordinary temperatures and under 
ordinary conditions. 

It is very soluble in water, and only sparingly soluble in 
40-per-cent. alcohol, the degree of solubility being about 
one part of the salt in one hundred parts of the alcohol of that 
strength. 3 

There is a basic baryta-salt, which is obtained by adding 
. baryta-water to the solution of the neutral salt and then preci- 
pitating by the addition of an equal volume of 84-per-cent. 
alcohol. The salt forms a white precipitate, which after dry- 
ing at 115° C. contained 42°84 per cent. of barium. The 
theory for (C,H, BaNOQO,),, BaHO,3H,O requires barium 
43°50 per cent. 

Cyano-propionate of Silver.—tThis salt is insoluble, or spa- 
ringly soluble in water. It was obtained by precipitating an 
aqueous solution of the baryta-salt by means of nitrate of silver, 
and formed a curdy white precipitate, which was washed, 
pressed between bibulous paper, and finally dried at 100° C. 
The dried salt was analyzed as follows : 

I. 0°397 grm., burnt with oxide of copper, copper-turnings, 
and a final stream of oxygen, gave 0°092 orm. of water and 
0:333 germ. of carbonic acid. 

II. 1:180 grm., burnt only for water, gave 0-245 orm. of 
water. 

ILI. 0:480 grm. gave, on ignition, 0°246 grm. of silver. 


(CO, H,N AgO,), 2(H, OQ). Found. 

Calculated. —— A —- 

(eS I. Dh: III. 

faxes 96 29-80 99-38. \ aa 

Teas isicis se a) 2°14 — 2°31 — 

ING. ane 28 6°65 — — — 
Wow ct Diet woieal ee 

On. 72 17-10 a 

ADL £00700 


The dry silver-salt was very hygroscopic, and absorbed 2 
per cent. of water very rapidly on exposure to the air. 

Apparently a basic silver-salt exists, and is obtained when 
basic baryta-salt is precipitated with nitrate of silver. Such 
a salt, dried in the water-bath, has given the following results 
on analysis :— 


Products of the Oaidation of Wool. 363 


(C,H, N Ag O,), Ag HO, H, O. 
Calculated. Found. 
yee oe — . 

Chix stents 96 LE30 17°90 a 
eee 11 200 BEN. Seley 

oy, @ovocoeesed 28 oe a ees 
Norges baveh 324 5838 Ly {B62 

Vesela 96 she ss 

BOD 


This basic salt requires further investigation. 

Cyano-propionate of Lead is insoluble, or sparingly soluble 
in water. It is obtained as a white precipitate on mixing an 
aqueous solution of the baryta-salt with an aqueous solution 
of acetate of lead. The precipitate was washed, pressed be- 
tween bibulous paper, dried at 100° C., and analyzed. 

0:463 grm., burnt with oxide of copper, gave 0°112 grm. of 
water and 0°374 grm. of carbonic acid. 


(©, BAN -PbO,).; A, 0. 

Calculated. 

————— Found. 

Cy -kaseiaaane 96 22°80 22°08 

Lg: ceageeaes 10 2°39 2°69 
IN, ~ sseesaaed 28 — 
Enly ast vader 207 — 
O; eeoeeosese 80 Ree 

421 


Cyano-propionate of Magnesia.—This salt was prepared by 
precipitating the baryta-salt by an equivalent of sulphate of 
magnesia, separating the sulphate of baryta by filtration, and 
evaporating the aqueous solution of the magnesia-salt in the 
water-bath. It is very soluble in water, and on drying at 
100° C. forms a jelly, which by very long-continued drying 
at 100° C. yields a brittle mass which may be powdered (giving 
a white powder). The powder was analyzed: 0°863 grm. 
yielded, on ignition, 0°132 grm. of magnesia, or 9°18 per cent. 
of magnesium. ‘The formula (C, H,N MgO,), 3H, O requires 
Mg per cent. =8°90. 

The magnesia-salt is very sparingly soluble in weak alcohol, 
an aqueous solution yielding a precipitate when it is mixed 
. with alcohol. 

Cyano-propionate of Potash, C,H,NKO,H,0 (dry at 
190° C.).—We have prepared this salt by taking a weighed 
quantity of the acid (dry at 100° C.), dissolving it in a small 
quantity of water, and then exactly neutralizing the solution 


364 On the Products of the Oxidation of Wool. 


with bicarbonate of potash: and we made the observation that 
the acid requires exactly the theoretical quantity of bicarbo- 
nate of potash in order to neutralize it. 

The resulting solution of potash-salt was evaporated to dry- 
ness in the water-bath, and formed a straw-coloured transpa- 
rent solid. It contained 21°68 per cent. of potassium. The 
formula (C,H, N KO,).5H,O requires 21:47 per cent. of 
potassium. When the salt is deposited from strong alcohol it 
dries up, at 100° C., to a solid containing rather less water, 
its composition being (C, H,N KO,).4H, O. Above the tem- 
perature of the water-bath and at temperatures below 140° C. 
there is a very gradual loss of water; and by prolonged and 
repeated heating to 190° C. half of the water is driven off, and 
the salt is found to have the formula 


C,H KO,, H, 0, 


which requires K per cent. 25°21. Hxperiment gave K per 
cent. 25°8. 

At temperatures higher than 190° C. decomposition began 
to take place, ammonia and a smell of organic cyanides being 
disengaged. The potash-salt undergoes decomposition before 
it parts with the last atom of water of hydration. 

As has already been indicated, the potash-salt is exceedingly 
soluble in water. It is also very soluble in 40-per-cent. alcohol; 
but in strong alcohol (84-per-cent. alcohol for instance) its 
solubility is very slight. 

When the potash-salt is heated for some time to temperatures 
between 200° and 220° C., with about one and a half times 
its weight of caustic potash, it undergoes decomposition appa- 
rently quite completely, and ethylamine is given off. On 
examination of the solid mass after the reaction was over 
we found that it conlained abundance of oxalate of potash ; 
but we found only minute traces of volatile organic acids. 
We proved also that the cyano-propionic acid had undergone 
complete decomposition. We looked carefully for succinic 
acid; and if present at all, it was not present in appreciable 
quantity. 

The reaction is 


C,H;NO, ++ 2KHO — C,0;K,0 + NCO,H, ; 


and accordingly the acid is isocyano-propionic acid. 
Cyano-propionate of Lime.-—We prepared this salt by heat- . 
ing an aqueous solution of the acid with excess of finely divided 
carbonate of lime, filtering to remove the excess of carbonate 
of lime, and evaporating the solution of the lime-salt in the 
water-bath. The salt, after being dried at 100° C. for some 


Notices respecting New Books. 865 


time, forms a brittle straw-coloured mass, non-fusible at 
100° C. The mass was dried at 100° C. till it became con- 
stant in weight. It was then analyzed: 0:3138 grm. contained 
0:1044 grm. of calcium, or Ca per cent.=12°84. The formula 


C,H,CaNO,, 2H,0 requires Ca per cent.=12°99. 


On raising the temperature this salt shows great stability; 


and a short heating to 200° C. drives off hardly 4 per cent., 


which is less than half an atom, of water. 

The salt is very soluble in water, and on mixing the aqueous 
solution with an equal volume of 84-per-cent. alcohol, gives an 
abundant powdery precipitate. No doubt this property might 
be taken advantage of to afford a means of purification. 


LVIII. Notices respecting New Books. 


Sur les Courbes dues & la Combinaison de deux Mouvements vibratoires 
perpendiculaires. Par M. A. Terquem. Lille: imprimerie L. 
Danel; 1879. (8vo, pp. 36.) 


pus paper is divided into four parts. In the first the Author 
states, by way of preliminary, the method of obtaining the 
equations to the Acoustic Curves by the use of Lisajous’s Cylinder ; 
in the second he investigates the properties of the curves as de- 
scribed on the developed surface of the cylinder; in the third he 
discusses the properties of the curves resulting from the projection 
of these cylindrical curves on a plane containing the axis— 
these projections being, of course, the acoustic curves themselves ; 
and in the fourth he obtains a method of making models of the 
eurves as drawn on the cylinder. His method is merely this :— 
He traces the developed curve on cardboard, and cuts it out, leaving 
it of a sufficient thickness ; he then bends it into the required form 
round a wooden cylinder, and gums the edges together; when the 
gum is quite dry he removes the cylinder; and on duly mounting 
the cardboard, which retains the cylindrical shape, he has the model 
of the curves. 
The substance of the paper is comprised in sixteen theorems, six 
relating to the cylindrical curves and ten to their projections. One 
of the chief of these theorems, relating to the projections, is the 
following :—‘‘ There exist in general 2mn—(m-+7) intersections, 
situated on lines parallel to the axes of # and z; some of these pa- 
rallels vary when A varies; others remain fixed” (p. 20). In this 
enunciation m is the number of rotations of the cylinder, n the 
number of oscillations of the molecule, and A+m the phase at the 
beginning of the time. In illustration of this theorem, the author 
draws the curves corresponding to ten values of A for m=4 and 
n=3, and for m=5 and n=3, 1. e. for a fourth and a major sixth. 
These curves, though more complicated, correspond, of course, to 
those given for the octave, twelfth, and fifth in Lord Rayleigh’s 
‘Treatise on Sound’ (vol. i. p. 29), which also would serve to illus- 


Phil. Mag. 8. 5. Vol. 7. No. 44, May 1879. 2k 


— 866 Notices respecting New Books. 


trate the theorem. On the whole, this is a very elegant paper on 
Acoustic Curves; it is needless to add that it is the work of an 
accomplished mathematician. 


American Journal of Mathematics, Pure and Applied. Editor m 
chef, J. J. Sytvester, LL.D., F.RS., Corr. Mem, Inst. of France. 
Associate Editor in charge, W1LtIaM EK. Story, Ph.D. (Letpsic). 
With the Cooperation of Brnsamin Prercey, LL.D., F_RS., in Me- 
chanics, Stuon Newcoms, LL.D., F.R.S., Corr. Mem. Inst. of 

France, in Astronomy, and H. A. Rowiann, C.H., in Physics. 

Vol. I. Baltimore: John Murphy and Co. (4to, pp. 388.) 

The Editors of this Journal have laid down very distinctly the 
object they have in view in its publication, and the kind of articles 
which it is intended to contain. It is designed in the first instance 
“asa medium of communication between American mathemati- 
cians,” though “its pages will always be open to contributions from 
abroad.” Its primary object is the publication of original investi- 
gations; but in addition concise abstracts will be inserted of sub- 
jects to which special interest may attach, as well as critical and 
bibliographical notices and reviews of the most important recent 
mathematical publications. 

The contents of the first Volume correspond very closely to the 
intention of the Editors. There will be found in it many very able 
original articles by American, and a considerable number by Euro- 

ean mathematicians; a few brief historical notes and extracts; 
while the bibliographical notices and reviews are represented by an 
elaborate paper on the “ Bibliography of Hyper-Space and Non- 
Euclidean Geometry,” and an excellent review, by Prof. Pierce, of An- 
nibale Ferrero’s exposition of the method of least squares. It would 
take us far beyond. our limits to notice even the leading articles of 
the volume; and there is the less need for us to do so, as some of 
them attracted considerable attention when the numbers contain- 
ing them were published—such as Prof. Sylvester’s “ Application 
of the New Atomic Theory to the Graphical Representation of the 
Invariants and Covariants of Binary Quantics;” and others are 
sure to be studied by those who devote special attention to the 
subjects to which they relate—such as Mr. Hill’s ‘‘ Researches in 
the Lunar Theory,” and Mr. Hddy’s articles on “‘The Theorem of 
Three Moments,” ‘‘The Elastic Arch,” and ‘The Two General 
Methods in Graphical Statics.” 

The form of the work is in every way worthy of its contents: 
it is printed on good paper, in a clear type, and, which is a capital 
point, is in quarto. This last circumstance will greatly imcrease 
the expense of the publication; and as a large number of subscri- 
bers cannot, perhaps, be expected, it is gratifying to learn that a 
considerable part of the pecuniary risk attendant on it has been 
guaranteed by the Trustees of the Johns Hopkins University. We 
hope that the Editors will find it possible to keep the succeeding 
volumes up to the very high level they have reached in the first. 


[ 367 ] 


LIX. Proceedings of Learned Societies. 


GEOLOGICAL SOCIETY. 
[Continued from p. 295. | 


March 26, 1879.—Henry Clifton Sorby, Esq., F.R.S., President, in 
the Chair. 


[HE following communications were read :— 

1. “ Results of a Systematic Survey (in 1878) of the Directions 
and Limits of Dispersion, Mode of Occurrence, and Relation to 
Drift-deposits of the Erratic Blocks or Boulders of the West of 
England and East of Wales, including a Revision of many years’ 
previous Observations.” By D. Mackintosh, Esq., F.G.S. 

The author’s researches lead him to the following conclusions :— 
Boulders from the North-Criffell range and Lake-district can be 
traced from the Solway Firth to near Bromsgrove (about 200 miles), 
and over an area in greatest breadth (from near Macclesfield to 
Beaumaris) of 90 miles, those from Criffell being particularly 
abundant near Wolverhampton. Boulders from the Arenig occupy 
a triangular area limited by a line drawn northward from Chirk to 
the Dee estuary, and to the 8.E. of that town are found as far as 
Birmingham and Bromsgrove. ‘The dispersion of the more distant 
Criffell Boulders would require submergences of from 400 to 1400 
feet ; of the Lake-district a little deeper ; while the distant dispersion 
of the Arenig Boulders took place at submergences between 800 
and 2000 feet. The author describes several of the more local 
drifts, and correlates the Lower Boulder-clay of the N.W. with the 
Chalky Boulder-clay of the east of England. He considers floating 
ice, not land-ice, to have been the agent of dispersion. 


2. “On the Glaciation of the Shetland Isles.” By B. N. Peach, 
Esq., F.G.S., and John Horne, Esq., F.G.S. 

After an account of previous opinion on the subject, the authors 
proceeded to describe the different islands, reviewing in succes- 
sion the physical features, geological structure, the direction of 
glaciation, and the various superficial deposits. From an exami- 
nation of the numerous striated surfaces, as well as from the dis- 
tribution of Boulder-clay and the dispersal of stones in that deposit, 
they inferred that during the period of extreme cold Shetland must 
have been glaciated by the Scandinavian Mer de Glace, crossing the 
islands from the North Sea towards the Atlantic. In the island of 
Unst, blocks of serpentine and gabbro are found in the Boulder-clay 
on the western shores derived from the rock-masses occurring on the 
east side of the watershed. Moreover, on the mainland between 
Scalloway and Fitful Head, blocks derived from the Old-Red-Sand- 
stone formation on the eastern sea-board are abundant in the 
Boulder-clay on the west side of the watershed. ‘The relative dis- 
tribution of these stones in the sections on the west coast is in direct 
proportion to the relative areas occupied by the rocks on the east 
side of the watershed. It was likewise pointed out that after the 

2E 2 


368 | Geological Soctety:—On the 


period of general glaciation Shetland nourished a series of local 
glaciers which radiated from the high grounds, the direction of the 
strie being at variance with the older system, while the morainic 
deposits also differ in character from the Boulder-clay progiees by 
the great Mer de Glace. 

The authors described the order of succession in the Old Red 
Sandstone formation in Shetland, and referred to the discovery of an 
abundant series of plant-remains in rocks which have hitherto been 
regarded as forming part of the series of ancient crystalline rocks. 
The plant-remains are identical with those found in the Old-Red- 
Sandstone rocks in Caithness, Orkney, and Shetland, from which it 
was inferred that the quartzites and shales in which the fossils are 
imbedded must be classed with this formation. The authors also 
described the great series of contemporaneous and intrusive igneous 
rocks of Old-Red-Sandstone age, adducing evidence in proof of the 
great denudation which has taken place in the members of this for- 
mation in Shetland. 


3. “On the Southerly Extension of the Hessle Boulder-clay in 
Lincolnshire.’ By A. J. Jukes-Browne, Esq., B.A., F.G-S. 

The southern boundary of the Hessle Clay has not hitherto been 
satisfactorily determined. ~The author traces this deposit along the 
border of the flat fen-land in South Lincolnshire, near Burgh, Steeping, 
&c., and the east and west Fen. He concurs with Mr. Searles 
Wood in believing the clay to be the product of shore-ice along a 
coast-line, and that the materials were in great part derived from 
the older ‘‘ Purple Clay.” He differs, however, from that author as 
to the correlation of the Hessle series, thinking this more probably 
older than the oldest river-gravels of the 8.E. of England. In an 
appendix a deep- well section at Boston is discussed, and reasons are 
given for assigning the greater part of the beds in this to the Jurassic 
Clays, not to the Glacial. 


April 9.—Henry. Clifton Soriy, Esq., FR. s., President, in the 
Chair. 


The following communications were read :— — 

1, “On ‘the "Geological Age of the Rocks of the Southern High- | 
lands of Ireland, generally known as ‘the Dingle Beds’ and ‘ Glen- 
gariff Grits.’ ” By Prof. KH.’ Hull; M.A.) ERIS.) EiGes: 

After reviewing the opinions of previous writers with reference 
to the age of these beds, including those of Hamilton, Griffith, 
Murchison, Kelly, Jukes, and the Officers of the Survey, which 
showed that great uncertainty has hitherto prevailed, the author 
quoted a passage of the late Prof. Jukes in which he confessedly 
left the determination of the age of these beds open for future 
examination; and he therefore determined to reinyestigate the 
question, bringing to bear upon it the knowledge which had since 
been acquired of other districts. For this purpose (and accom- 
panied by Messrs. O’Kelly and M‘Henry) he examined a series of 
sections, from the coast of Dingle southwards to Bantry Bay, and, 


Age of “ the Dingle Beds” and “ Glengarif’ Grits.” 369 


having also carefully examined the field-maps of the Survey of 
those districts, had arrived at the following results :— 

First, that “the Dingle Beds” are perfectly conformable to, and 
continuous with, the Upper Silurian Beds of the Dingle promontory. 

Secondly, that they are the representatives of “the Mweelrea 
Beds and Salrock Slates” of West Galway and Mayo, the age of 
which, as shown by the fossils,is Upper Silurian, and that “the 
Dingle Beds” may therefore be regarded as of the age of the Ludlow 
Rocks, but unusually developed. This view was adopted as far back 
as 1839 by Sir Richard Griffith. 

Thirdly, that throughout the south of Ireland ‘the Dingle and 
Glengariff Beds”’ are disconnected from the succeeding conformable 
series, consisting of (c) Lower Carboniferous Slate, (6) The Upper 
Old Red Sandstone with Anodonta Jukes, (a) The Lower Old 
Red Sandstones and Conglomerate, as these three conformable 
formations are found resting upon, and against, the Glengariff beds 
successively in a direction either from south to north, or from 
south-west to north-east, owing to a conformable overlap against 
the flanks of an old shelving shore formed of the Glengariff beds. 

Fourthly, that at the close of the Upper-Silurian period, and 
_ after the deposition of ‘“‘the Dingle and Glengariff Beds,” these 
strata were disturbed, upraised, and denuded, and were not again 
submerged till the commencement of the Old Red Sandstone (a), 
when they were successively overlain by the beds of that formation 
with the succeeding ones of the Lower Carboniferous period, pro- 
bably including the Carboniferous Limestone in some places. 

Lastly, that it was during this period of upheaval that, as the 
author believes, the marine Devonian Beds (Ilfracombe and Morte 
series) were deposited, which accounts for their absence in the 
Trish area, which was either a land surface or only partially sub- 
merged. To this part of the subject the author hoped to call the 
attention of the Society on a future occasion. 


2. “On some Three-toed Footprints from the Triassic Conglo- 
merate of South Wales.” By W. J. Sollas, Esq., M.A., F.G.S. 

The author described the discovery by Mr. T. H. Thomas of 
some three-toed footprints in the Triassic Conglomerate at Newton 
Nottage, South Wales. They were stated to resemble in their most 
important characters the footprints of some Ratite birds, such as 
the Emu; and this fact, taken in connexion with the occurrence 
of Dinosaurian remains in the Magnesian Conglomerate of Bristol, 
led the author to attribute to them a Dinosaurian origin. 


3. “On the Silurian District of Rhymney and Pen-y-lan, Cardiff.” 
By W. J. Sollas, Esq., M.A., F.G.S. 

The paper commences with a history of the previous observations 
on the district; a description of the geographical distribution, geo- 
logical structure, and vertical succession of the Silurian rocks is next 
given. They comprise beds belonging to the Wenlock and Ludlow 
groups, and pass conformably upwards into the Old Red Sandstone. 
The district affords a good base for a measurement of the thickness of 


370 Intelligence and Miscellaneous Articles. 


the Old Red Sandstone on the south of the South-Wales Coalfield. 
This was found to be a little over 4000 feet. The thinning-out of 
the Old Red Sandstone and Silurian strata, together with the marked 
change which takes place correspondingly in the lithological cha- 
racters of the latter formation on passing from the north to the 
south side of the coalfield were taken to indicate an approach to a 
shore-line. This shore-line belonged to land which, as shown by the 
great thickness of the Devonian beds, could not have extended far 
south. It corresponded to Mr. Etheridge’s barrier between the Old- 
Red-Sandstone and Devonian seas. ‘The sandstones with Old-Red 
characters, such as the Hangman Grit and the Pickwell-Down 
Sandstones, occurring in the Devonian formation were deposited at 
intervals when this barrier was submerged to a greater depth than 
usual. The Cornstones were stated to thin out to the south along 
with the other sedimentary beds of the Old Red Sandstone, and 
were regarded as derived from the denudation of previously up- 
heaved limestones, such as the Bala and Hirnant. The paper con- 
cluded with a description of the characters of the more interesting 
rocks and fossils. 


LX. Intelligence and Miscellaneous Articles. 


ON THE OPTICAL PROPERTIES OF STARCH. 
To the Editors of the Philosophical Magazine and Journal. 

GENTLEMEN, Vienna, March 31, 1879- 

HE January Number of the Philosophical Magazime contains a 

paper by Mr. Walter Baily, in which he refers to a former paper 

of his, ‘‘ The Optical Properties of Starch,’ Phil. Mag. for August 

1876. This paper having at the time escaped my notice, I hope 

you will now allow me a few remarks on this subject in your 
Journal. 

In the year 1864 I published in Poggendorff’s Annalen, vol. exxiil., 
a note, ‘‘Ueber das Kreuz, das gewisse organische Korper im 
polarisirten Lichte zeigen, und tiber die Haidinger’schen Farben- 
biischel.” I there showed that the cross which starch, the crystal- 
line lens, sections of horn, &c. give in the polarizing microscope 
may be explained by a radial structure of doubly refracting mate- 
rial. 

I proved this also by experiment, by rotating a sector of mica 
between two Nicol prisms. Using instead of mica a dichroic 
mineral and only one Nicol, a cross is obtained the alternate 
branches of which are differently coloured. In the same paper 
. I made use of this fact for an explanation of Haidinger’s brushes. 

At a later period I had a mica disk, formed of sixteen sectors, all 
identical and cut symmetrically to the optic axes, constructed 
by M. Steeg, of Homburg. This disk showed the cross very well 
in the old Norrenberg apparatus, especially when by a suitable 
lens the bounding lines between the different sectors were rendered 
a little indistinct. 


Intelligence and Miscellaneous Articles. 371 


Another way of producing this cross depends on the fact that 
glass becomes doubly refracting by pressure. In pressing, there- 
fore, a lens against a plate of glass, all the conditions for the cross 
are fulfilled. A little contrivance for this purpose was described 
by me in Carl’s Repertorium, vol. i. p. 376. 

I am, Gentlemen, 
Yours faithfully, 
VIKTOR V. Lane. 


ON THE MAGNETIC ROTATORY POWER OF VAPOURS. 
BY E. BICHAT. 


By causing the current supplied by 80 large Bunsen cells to act 
upon aray of polarized light traversing vapour of sulphide of carbon, 
I ascertained an evident rotation of the plane of polarization. The 
rotation was very slight, not exceeding 15'. The first experiments 
which led me to the result I have just indicated were made in the 
course of the month of July 1878. 

The apparatus was constructed by M. Ducretet, of Paris. It 
consists of two concentric tubes of 3°6 metres length. The inner 
tube is closed by parallel glass plates, and carries two tubulures 
furnished with cocks permitting it to be put in communication with 
the outside. In the annular space comprised between the two 
tubes a current of hot water, or a current of oil, or a current of 
vapour can be made to circulate. For a length of 3 metres the 
tube carries a series of bobbins covered with wire 3 millims. in 
diameter. Experience shows that under these conditions the action 
of the current upon the glass plates is ni. 

By means of the same instrument I have been able to prove in 
the same manner an evident action of the electric current upon 
polarized light passing through the vapour of bichloride of tin. 

I have done more: I have followed, step by step, from zero to 
the temperature of ebullition, the rotation of the plane of polariza- 
tion produced by one and the same current acting on sulphide of 
carbon and bichloride of tin. I have thus ascertained that the 
molecular rotatory power is maintained as long as the vicinity of 
boiling-point of the liquid is not reached. At that moment there 
is a diminution much more rapid than could have been foreseen 
from the calculation based on the knowledge of the ratio of the 
densities. 

I should have liked, before publishing the results of these 
researches to be able to establish in a rigorous fashion the relation 
that exists between the magnetic rotatory power of a liquid and 
the rotatory power of its vapour. For this it would have been 
necessary to be able to augment the action produced by the latter, 
and at the same time to improve the measuring-processes. It has 
not yet been possible for me to do so. I nevertheless hope soon to 
overcome the difficulties which have hitherto stopped me. 

If I decide to publish now these still incomplete results, it is 


372 Intelligence and Miscellaneous Articles. 


because I have just read in a foreign scientific journal* an account 
of similar experiments made at Strasburg with apparatus arranged 
like that which I have just described. In those experiments MM. 
Kundt and Rontgen ascertained, without being able to measure it, © 
the magnetic rotatory power of sulphide of carbon, sulphuretted 
hydrogen gas, and gaseous sulphurous acid. 

There is, however, a considerable difference, in respect of the 
results that can be obtained by this method, between the apparatus 
which I use and that employed by the German physicists. This 
difference arises from the nature of the tube for containing- the 
vapour. My tube is of brass, while that at Strasburg is of iron. 
This latter therefore constitutes a large hollow electromagnet haying 
in its interior the gases which are to be investigated. 

To show the inconvenience presented by such an arrangement, I 
will cite the following experiment. A tube filled with sulphide of 
carbon is placed between the poles of a Faraday electromagnet ; it 
gives a rotation of 10° 30’. On introducing this tube inside one 
of the two hollow electromagnets of the same apparatus, and 
passing into this single electromagnet the whole current of the pile, 
‘ no appreciable rotation is observed. 

Tt is true that when the iron tube of the electromagnet is thinner 
the action is not entirely annulled; but it is always considerably 
diminished. Thus a hollow bobbin 20 centims. m length, con- 
taining a tube filled with sulphide of carbon, gives a rotation of 5° ; 
if an iron tube of 2°5 millims. thickness be placed in the bobbin, the 
rotation is not more than 1°. 

These experiments, moreover, only confirm the theory of hollow 
magnets, given by M. Bertin nearly twenty-five years since t.— 
Comptes Rendus de V Académie des Sciences, March 31, 1879, 
t. lxxxviil. pp. 712, 713. 


ON AN ELECTRICAL BURNER AND BLOWPIPE. 
BY M. JAMIN. 

The electric are that springs between two carbon conductors is a 
true current. When submitted to the near influence of a current, 
a selenoid, or of a magnet, it undergoes an action governed by 
Ampeére’s laws, identical with that which would be undergone by 
any metallic conductor put mits place; but as the mass of the 
material of which it consists is very little, the velocities it takes are 
considerable. It can be attracted, repelled, displaced, fixed, caused 
to rotate—in a word, made to go through all the motions that can 
be impressed upon movable currents in electromagnetic experi- 
ments. The first action of this sort was observed by M. Quet, who 
projected horizontally, in the shape of a dart, a vertical are between 
the two horizontal poles of an electromagnet. A multitude of 
similar experiments can be made; I shall today content myself with 
citing the following. 

* Wiedemann’s Annalen, 1879, No. 3, p. 332. See Phil. Mag. March 
1879, p. 178. 

Tt Ann. de Chim, et de Phys, (8) Wiii. p. 90. 


- communicating with the poles of a pile ora 


. the first two and then taken away. J then 


Intelligence and Miscellaneous Articles. 373 


I place vertically two carbons AB, A'B’, p_—> & 


Gramme machine; I light the arc in C by 
means of a small carbon introduced between 


place behind the south pole of a magnet pro- 
jected in O, or the north pole in front, or both 
at the same time. We know that, according to 
Biot and Savart’s law, the element of current ¢ 
must be displaced toward its right, looking at 
the south pole ; and experiment shows that the 
arc immediately moves as far as the base B B’ of 
the carbons; it reascends, on the contrary, to 
to the summit A A’ if the magnet be turned. It then becomes 
fixed at the summit, but changes shape: it curves, and spreads out 
into a sheet with pretty intensely loud hummings. If the magnet 
is powerful, the are is as it were blown upwards, and finally dis- 
appears after taking the shape of an elongated flame. 

The same thing happens if we surround the two carbons with a 
rectangle, CD EF, traversed by the same current. Each of the 
parts of this rectangle cooperates in raising the arc if the direction 
of the current is the same in the carbons and in the rectangle, and 
in causing it to descend if the directions are contrary. The action 
is multiphed by the number of turns given to the outer wire. 
Four turns are sufficient to fix the are in A <A’; and it remains 
there, whatever be the position given to the apparatus, even when 
the points are directed downwards. 

It is evident that in this experiment the arc can be kept in A A’ 
and all insulating material omitted between the carbons. When 
the operation takes place with a continuous current of constant 
direction, the positive carbon burns more brightly, is more quickly 
consumed, and diminishes in length; the are is maintained at and 
descends with its extremity. The negative carbon burns only in 
its interior ; it diminishes in thickness, but keeps its length entire, 
and may serve foranother time. When machines with alternating 
currents are employed, of which the direction changes at the same 
time in the carbons and in the rectangle, the action keeps the same 
sign; in spite of the inversions, the are is always kept at A A’; 
and the carbons undergoing equal wear, their points remain always 
at the same level, as in the Jabloschkoff candle. 

It remains to know how the arc can be lighted at the beginning, 
and relighted if it happens to be extinguished. For this purpose I 
render the carbons movable about two joints A’ and B’, with a 
spring to reunite them at their summit, and two buttresses to pre- 
vent too wide separation between them. Under these conditions 
the carbons repel one another, being traversed by opposite currents. 
Moreover C D attracts A B, and repels A’ B’, while E F performs 
the inverse action. All these effects concur to separate the 
carbons, which recede spontaneously. They ignite immediately the 
current commences, keep apart as long as it continues, to rejoin cne 


B74 Intelligence and Miscellaneous Articles. 


another whenever it ceases. In short, this is a completely automa- 
tic candle requiring only a very simple support; the lighting, the 
fixing at the desired distance, and the maintenance of the arc at the 
two points result spontaneously from the electromagnetic forces, 
which take upon themselves the whole of the work. It is moreover 
evident that these forces are proportional to the square of the 
intensity of the current, and can always be rendered sufficient; it 
is only a question of construction. M. Fernet proposed to place 
the carbons one in the prolongation of the other, and to take 
advantage of their repulsion to separate them. This repulsion was 
but feeble; in the solution proposed by me the action is more 
energetic and becomes efficient. 

When the action of the rectangle is sufficient, the arc, spread out 
and driven beyond the points, has the appearance of a gas-flame ; 
its length is increased. From this results a greater expenditure of 
electromotive force; and the amount of light is not increased pro- 
portionately ; for itis known that, if the are attains a very high 
temperature, it does not possess a brightness comparable with that - 
of the carbon points. But on remarking that the are was projected 
outside, I conceived the idea of receiving it upon lime, magnesia, or 
zircon, like the oxyhydrogen-flame in the Drummond lamp. The 
arc is crushed by this obstacle, keeps a constant length, and, far 
from consuming more electromotive force, it saves a notable portion, 
because it springs in a highly heated and more conductive space. 
On the other hand, the light, instead of disappearing skywards, 
where it is useless, is reflected toward the ground; this will permit 
the electric lamp to be placed at a great elevation, out of the usual 
direction of looking. Besides, the light is altogether changed: it 
is no longer violet, but white ; it even appears greenish yellow by 
contrast and by the augmented intensity of the green lines of the 
lime; and, finally (the most valuable result of all), it is at least 
three times as intense as without the cap of lime. In truth, that 
cap must not rest upon the points; for these will fuse and pene- 
trate the lime, and the are will find its path inwards and shine no 
more. ‘This defect can easily be remedied. 

The fusion of the lime proves that the arc thus projected by a mag- 
netic effect is capable of considerably heating all bodies ; it is a real 
blowpipe—probably the most powerful of all. I recommend it to 
chemists and physicists. I shall myself have to entertain the 
Academy with the powerful effects that can be obtained from it.— 
Comptes. Rendus de ?Académie des Sciences, March 17, 1879, 
t. Ixxxvii. pp. 041-544. 


ON THE ELECTRICAL PERFORATION OF GLASS. 
BY PROF. A. VON WALTENHOFEN. 

In connexion with his experiment described in 1866, and with a 
treatise referring to it, by H. Mach and 8. Doubrava, just published, 
the author describes the following additional experiments :— 

A thin glass plate having upon it ever so small a drop of 
stearine, introduced into the path of the spark of an electrical 


Intelligence and Miscellaneous Articles. 375 


machine, is perforated at that place, and more readily if the side on 
which the drop lies be turned towards the posztive electrode. 

A glass plate with bifilar suspension between the electrodes of a 
Holtz machine is driven by the discharge toward the negative elec- 
trode, and, indeed, with more force if the side turned to the positive 
electrode is partially coated with stearine. 

Fixed points for an explanation of these facts are found by the 
author in the assumption, once previously enunciated, and on that 
occasion also advocated by G. Wiedemann, that the air molecules 
in the spark’s path are affected, in their certainly very energetic 
motions, with a velocity-component directed from the positive to 
the negative electrode, such as was originally attributed by Plucker, 
and after him by Reitlinger, to the positive electricity itself— 
Karserliche Akademie der Wissenschaften in Wren, math.-naturw, 
Classe, March 6, 1879. 


ON THE PRESSURES EXERTED BY GALVANIC DEPOSITS. 
BY M. BOUTY. 


If we take a thermometer with a cylindrical reservoir, render it 
conductive by coating it with gold leaf or thinly silvering it, and 
employ it as the negative electrode in the decomposition of a 
copper-salt (for instance), the metallic deposit exerts a considerable 
pressure upon the reservoir ; for the mercury rises in the stem the 
more as the deposit is thicker. And to explain this ascent one can 
neither invoke a local rise of temperature, which is insignificant— 
nor an electrical action properly so called; for the thermometrical 
excess has no direct relation with the intensity of the current, and 
persists integrally after the suppression of the latter. It depends 
exclusively on the more or less perfectly metallic quantity of the 
deposit, and will probably be capable of supplying the indirect 
measure of it. Very crystalline or coarsely granular deposits 
exert but a trifling compression. When we dissolve the metal 
with an acid the thermometer becomes normal again. 

Professor Mills*, who discovered before I did, and without my 
being aware of it when I commenced this investigation, the fact of 
the contraction of thermometers, announced that copper, silver, 
iron, and nickel contract, and that cadmium and zine dilate the 
reservoirs upon which they are applied. JI have found that all 
metals, including zine, always act only by pressure ; but the pressure 
is not necessarily normal, or the same at all points, and cannot 
serve directly as a measure for the phenomenon. It is the result 
of a change of volume undergone by the metal in being deposited. 
I shall confine myself to the establishment of this point, reserving 
for an ulterior Note all the peculiarities I have observed. 

Let us imagine that a cylinder M of external radius R and 
indefinite length becomes covered witha regular solid coat of which 
the external radius is R’. It undergoes a shrinkage, the amount 
of which would be a fraction «@ of its internal volume if the cylinder 
M offered no resistance ; but as it does resist, a normal pressure 


* Proceedings of the Royal Society, vol. xxvi. p. 504. 


376 Intelligence and Miscellaneous Articles. 


P is developed at all points of the contact-layer, acting from with- 
out inwards upon the cylinder, from within outwards upon the 
deposit. It is easy to demonstrate the formula 


a 


Pees (1) 
m+ 5 (qe :+5) i 


in which m represents the unit diminution of external volume of 
the cylinder under an external pressure equal to unity, & the com- 
pressibility-coefficient of the metal. 

(1) If the deposition is produced by a current of constant inten- 
sity distributed uniformly over the whole surface of the cylinder, 
the weight of copper deposited upon unit length has for its expres- 
sion (D designating the density of the copper, and p a constant) 


pt=7(R?= BD, .... .. ee (2) 
whence ee 
he m+3 k os At 
iP — ee ot) ps — ae ost vw © vw we (3) 


3 m+k Pp 


I have verified that not only my experiments, but also those of 
Prof. Mills, are very exactly represented by empiric expressions of 
this form. 

(2) The limit A towards which the pressure for a deposit of in- 
definite thickness tends is independent of R; but B is not so: the 
shorter the radius R, the more rapidly does the pressure approach 
its limit. Experiment shows, in fact, that the contraction of an 
almost linear thermometer is very rapid; while I have observed 
only a trifling contraction of a large alcohol thermometer of 3 cen- 
tims. diameter, although it had an extremely capillary stem. 

A thermometer, the cross section of which is a very flat ellipse, 
will be submitted to pressures rapidly increasing at the extremities 
of the major axis of the ellipse, where the curvature is considerable ; 
and its section will become more nearly circular; the mercury will 
descend in the stem, while it would rise if the same thermometer 
had been compressed in a piezometer. 

(3) I have had made, by M. Alvergniat, some cylindrical ther- 
mometers with much-elongated reservoirs, of known internal and 
external radii, and swollen at the origin of the stem, so that they 
could be fitted, in place of the gas-reservoir, into the apparatus 
constructed by M. Ducretet for the experiments of M. Cailletet. 
After determining experimentally their internal, from which I de- 
termined by calculation their external compressibility m, I sub- 
mitted them to coppering in the centre of a Daniell’s cell of the 
same height as the reservoir. Then observing from hour to hour 
their excess, I was able to determine empirically the coefficients A 
and B of the formula (3), and hence to deduce X. The mean of 
fifteen series of experiments, made with three different thermome- 
ters, gaye :— 


Intelligence and Miscellaneous Articles. a7 


Thermometer. oss... k=0:0000012179 
ce aah Cape ae 0:0000012245 » 
F Si ans Bea 0:0000012360 


Mean .. 0:0000012351 
M. Reegnault found directly for cold-beaten red copper 
k=0:0000013817. 


(4) The diminution of volume varied between much wider limits 
than &. The highest value I have calculated is z=0:000865. Ad- 
mitting this number, the greatest pressure that could be developed 
by a deposit of copper on an absolutely resisting cylmder (m=0) 
would be nearly 300 atmospheres. In reality 1 have not yet ob- 
served pressures above 100 or 110 atmospheres. 

Lam still pursuing these researches, for which M. Jamin has 
placed at my disposal all the resources of his laboratory.— Comptes 
Rendus de V Académie des Sciences, March 18, 1879, t. Ixxxviil. pp. 
714-716. 


NEW ESTIMATE OF SUN’S DISTANCE. 
BY PLINY EARLE CHASE, LL.D. 
In accordance with the principles of my spectral harmonics, 
Lockyer’s fundamental “ basic line” (4215 ten-millionths of a mil- 
limetre) gives the following equation :— 


Earth’s orbital unit © el 
fundamental unit ( ® radius/ © 


This gives 93,700,000 miles for Sun’s distance. 

The “ orbital unit” is the mean orbital movement of Earth while 
a body at Harth’s equatorial surface falls through the increment 
of the fundamental line. 

Lockyer’s “basic lines,” Peirce’s meteoric hypothesis, and my 
demonstration of the influence of light in world-building and mole- 
cular grouping lead to the equation of mass— 


Jupiter? = Sun x Earth x Saturn. 
This equation gives the following values :— 
Sun’s mass = 328,600, 
» distance = 92,549,000 miles, 
jo parallax ==" 8" 8322. 


Haverford College, Pennsylyania, Puiny EH. Cuase, 
March 25, 1879. 


CONTRIBUTION TO THE THEORY OF THE MICROPHONE. 
BY HERMANN ARON. 
The microphone is based, as is well known, upon the fact that 
vibrations produce in it alterations of the resistance, whence arise 
fluctuations of current which are percetyed by means of a telephone. 


378 Intelligence and Miscellaneous Articles. 


In the following the case shall be treated of the fluctuations of re- 
sistance being indefinitely small in comparison with the total resist- 
ance; and the reaction of the vibrating plate upon the conduction, 
by which at all events only current-waves of inconsiderable strength 
compared with the original ones are produced, shall be neglected. 
The equation representing what takes place then becomes 


TW=E-Q&, 


Here E signifies the electromotive force of the battery employed, 
W the resistance, J the intensity of the current, and Q the electro- 
dynamic potential of the circuit upon itself. 

We now put W=W,+4+w, J=J,+7. W, and J, denote resist- 
ance and current-intensity in the state of repose, w and 2 their 
variations during the vibrations ; w and 2 are, according to our hy- 
pothesis, small quantities. After this substitution our equation 
becomes | | 


(T,+A(W, tw) =E-QSeo 49), 


If we take into account that J,W,=H, that iw is a small quantity 
of the second order, which in comparison with those of the first 
UJ,+2) dh 


a Ge ow equation as- 


order we will neglect, and that 


sumes the form 


See Wi Q 5 50. (1) 


To this equation we can attach the following remark. If w, and 
7,, as well as w, and 2,, are two systems of waves which satisfy the 
equation, then w,+w, and 2,+7, also satisfy it; that is, the differ- 
ent wave-systems are superposed without mutual disturbance. The 
microphone must necessarily possess this property if most of the 
influences operating upon it are not to express themselves entirely 
or for the most part as noises ; and not only so, but it follows from 
the assumption of very small changes of resistance in proportion to 
the total resistance, because thereby the equation became linear ; 
consequently we see that the fulfilment of this condition is also ne- 
cessary in practice for the good rendering of a sound. 

If we now analyze each vibration into summands according to 
Fourier’s series, we need only treat the summands singly. Accord- 
ingly let w= A sing 27, let the current-wave belonging to it be 


=e (q2n+ é), 
so that we assume the phase-change 6; this, introduced into equa- 
tion (1), yields 


J A sin fn 27+ W,B sin é Qa-+ :) + an QB 


T cos (q27+8)=0. 


Intelligence and Miscellaneous Articles. ate 


: aut t 
If we develop the left side according to sin and cos and put 


T i 
their factors singly =0, we get two equations for B and 6:— 
J,A+ WB cos 8— =22° sin 3=0; 
W,Bsin 9+ 222" cos 8=0. 

From the last equation it ae that 
27Q. 

Seen Pu wath exc popccss ater st Res 2 

tan 6 Wt (2) 


The change of phase is therefore the greater the smaller T is—that 
is, the higher the tone is. or the amplitude we find 


AJ, cos é 
W, 
or 
5 AE x 


Mi. J 4eQ 
oe Me Wop WoT? 


From this formula it follows that the amplitudes are not all altered 
in equal measure, but they become proportionally smaller for tones 
for which a is greater. But this becomes smaller for T greater ; 
that is, the higher the tone the smaller will be its amplitude ; and this 


3, 9 
— is—that is, the less 


the resistance and the greater the value of Q the electrodynamic 
potential. Large coils, therefore, especially with iron cores, operate 
prejudicially. 

In his article “Telephon und Klangfarbe”*, Helmholtz showed 


2(-)2- 


is so much the more the case the greater 


that with the telephone also it depends on the expression WoT 
0 


but in exactly the inverse sense, so that in the telephone the higher 
tones have the advantage over the deeper ones—thus giving the 
peculiar result, that in the telephone the tone ts heightened, but in the 
microphone rt 1s made deeper. 

A combination of the telephone with the microphone can now be 
produced in which the electric conveyance operates generally no 
change in the tone. This combination is to serve for the giving, 
while for the receiving instrument a telephone is made use of in 
the usual manner. If we further denote by M the fluctuation of the 
magnetic moment in the telephone of the giver, we find the follow- 
ing as the equation for the current-waves excited by means of such 


a system, in accordance with the above way of considering the sub- 
ject :-— : dM dt 

Jwt+Wi=- ope ee 

* Wied, Ann. v. p. 448 (1878). 


380 Intelligence and Miscellaneous Articles. 
And putting 
w= A sin s 27, 
eX 
t 
as 


1=Csin (7 20), 
we get for the determination of C and 6 the following equations, 


“7 QC sin 8— WC cos 8=J,A, 


M= Bein 2x. 


WW, Csin d+ 7 QC cos yeas =a 
from which follows 
2 

= (JAQ—W.B) 


Csin 0= TT ; 
Wit se @ 
J.W,A+ 7% BQ 
Ccos d= — TH 
2 v 2 
Vi 7 Q) 
If the ratios be chosen (as can be done in various ways) so that 
J AQ—W,B=90, 
then a) 
and C=—J,A. 


Thus the electrical conveyance will not introduce any alteration 
either of the phase or in height or depth of tone—Wiedemann’s An- 
nalen, 1879, No. 3, vi. pp. 408-407. 


Charlottenburg, December 1878. 


ON THE VARIATION OF THE THERMAL CONDUCTIVITY OF METALS 
WITH TEMPERATURE. 


To the Editors of the Philosophical Magazine and Journal. — 


GENTLEMEN, 

Dr. Hopkinson has kindly pointed out to me, in my last paper 
published in your recent issues (March and April), a slip of a fun- 
damental character, which [ am sorry to say renders the latter half 
of that paper questionable, if not, as I fear, erroneous. I hope 
shortly to be able to find time to go through the calculations again 
-and make the necessary modifications ; but in the meantime I must 
beg your readers to treat the paper as if it had not yet appeared. 

IT am, Gentlemen, 
Your obedient Servant, 
April 7, 1879, OLIvER J. LODGE. 


Pi Sas. bal ae Seas 


THE 


LONDON, EDINBURGH, axv DUBLIN 
PHILOSOPHICAL MAGAZINE 


AND 


JOURNAL OF SCIENCE. 


[FIFTH SERIES.] 


JUNE 1879. 


LXI. On the Thermal Conditions and on the Stratification of 
the Antarctic Ice. By O. Fisuer, Clk., M.A., F.G.S.* 


IR WYVILLE THOMSON delivered a lecture at Glas- 
gow, November 23, 1876, “On the Condition of the 
Antarctic” t. In it he gave a most interesting and graphic 
account of observations made during the visit of the ‘ Chal- 
lenger’ to high southern latitudes. Towards the conclusion 
of the lecture, the author advanced some speculations about 
the probable thickness and physical conditions of the antarctic 
ice-cap. There appeared also in the ‘Quarterly Journal of 
Science’ for January last an article from the pen of Dr. Croll, 
which contained certain criticisms upon the conclusions arrived 
at by Sir Wyville Thomson, and giving reasons why the ice-cap 
may be considerably thicker than that philosopher supposes. 

I venture to think that there are a few points left in a some- 
what uncertain state by both these gentlemen, which a little 
mathematical treatment, of by no means an abstruse nature, 
may assist in clearing up. 

The first of these relates to the limit of thickness which the 
effects of temperature might impose on the antarctic ice. 

Dr. Croll remarks that there are but three sources from 
which the ice-cap can receive an appreciable amount of heat, 
viz. (1) the air above, (2) the earth beneath, (3) the work of 
compression and friction. The last of these he dismisses as in- 
considerable, and without doubt rightly so. 

* Communicated by the Author. 
+t ‘Nature,’ vol. xv. pp. 102, 120. 
Phil. Mag. 8. 5. Vol. 7. No. 45. June 1879. 2G 


382 Mr. O. Fisher on the Thermal Conditions and 


Sir Wyville Thomson remarks that “it is not easy to see 
why the temperature of the earth’s crust, under a widely ex- 
tended and practically permanent ice-sheet of great thickness, 
should ever fall below the freezing-point.”” Our first inquiry 
therefore shall be :— 

(1) [fa level sheet of ice rest upon the earth, its upper sur- 
face being maintained at a uniform mean temperature lower 
than the freezing-point, to find the thickness beyond which melt- 
ing at the lower surface must take place. 

It is assumed that the form of the ice-cap 1s permanent; so 
that we may consider that the masses, whether of rock or ice, 
have arrived at that state in which the temperature is also 
permanent. Probably any horizontal movement in the ice, 
so long as the thickness at any place remains unaltered, will 
only very slightly affect this supposition—because, if there be 
sliding of the parts one over another, ice abstracted by hori- 
zontal movement will be replaced by ice at the same tempe- 
rature. 

We know that there is a continual flow of heat out of the 
earth. This flow is such that it is found to raise the tempe- 
rature of the strata of the earth by about 4, of a degree Fahr. 
per foot on descending. This average increase prevails equally 
wherever observations have been taken. Hven at Yakoutzk, 
where the ground is perpetually frozen beyond the depth 
pierced, the same rate obtains. This may therefore be ad- 
mitted as an empirical fact. But the following reasoning may 
perhaps be accepted as explanatory of this uniformity of rate. 

If the temperature of the surface of the earth were suddenly 
lowered at any place, the flow of heat to the surface would by 
that means be temporarily increased, and therefore also the 
rate of increase near the surface. But since the general in- 
ternal temperature is no greater below that locality than else- 
where, this increased flow near the surface must take place at 
the expense of the superficial strata. Hence the isogeotherms 
near the surface, though temporarily brought closer together, 
will shortly begin to separate again, until the rate of increase 
falls to its normal value. At this juncture the flow of heat at 
the surface at the place in question will become equalized to 
that which obtains elsewhere. And since the supply of heat 
from the interior is the same here as elsewhere, the rate can 
fall no lower, and -will afterwards continue equal to that which 
obtains in other regions. It follows that the permanent rate 
of increase of temperature near the surface of the earth will 
be everywhere the same, and the flow of heat also, whatever 
the temperature of the surface may be. This is what obser- 
vation shows to be the case. 


on the Stratification of the Antarctic Ice. 383 


It is evident that this result will be independent of the 
cause which maintains the temperature of the surface (say) 
below the average, whether it be a cold climate or an ice- 
sheet. We may therefore assume that the rate of increase in 
the earth beneath the ice-sheet is gy of a degree Fahr. per foot 
of descent. 

Let us now suppose that our sheet of ice is throughout 
below the melting-temperature, so that the level of that cru- 
cial temperature is situated within the rock. In this case the 
flow of heat from the earth will pass into the ice unaltered in 
amount, because none of it will be arrested and consumed in 
melting ice at the junction. The ice will then be under con- 
ditions which will render it sufficiently amenable to the fol- 
lowing statement of Fourier:— 

“The thermometric state of a solid enclosed between two 
parallel infinite planes, whose perpendicular distance is e, and 
which are maintained at fixed temperatures, a and 5, is repre- 
sented by the two equations ”’ 


v=a— ar? (e—2), ae Nese gt 
a—b | 
B=f : | 

or a fittleni %) Nal2Ra ies Homa wue) 
ss | 


where, for convenience in the present instance, we have taken 
the origin of z (the depth) at the surface. 

v is the temperature at the depth z, 

a 5 di of the lower surface, 

> = of the upper surface, 

k the conductivity, 
and F' is the flow of heat upwards through the solid. 

The last of these equations will be applicable to the rock if 
the proper value be assigned to hk. 

Let K be the conductivity of rock, 

k + A ice. 


d 
Now - represents the rate at which the temperature in- 


creases in descending. We know that for rock this is gy, the 


units being the foot and degree Fahr. Suppose £8 to be the 
d : ‘ 
value of = for the ice; F will be, under the circumstances 


2G 2 


384 Mr. O. Fisher on the Thermal Conditions and 


supposed, the same both for the ice and rock. Hence equa- 
tion (2) becomes, 


1 
for the rock, F=K 50" 
for the ice, F=f, 
whence | 
y aaa 
~ k 60 


Now the ratio of the conductivities will be the same whatever 
system of units we employ. » 

Referring to Professor Everett’s ‘ Illustrations of the C.G.S. 
System of Units,’ we find the mean of K for three kinds of 
rock in situ, as determined by Sir Wm. Thomson, to be 00581, 
and the mean of & for ice ‘(00218 ; whence 


ean 
~ 218 60 
= "04441, 

Hence, for the ice, 
= = 04441, 


in which expression a is the temperature of the surface in con- 


- tact with the rock, and 0 is the temperature of the surface ex- 


osed to the air, e being the thickness of the ice. 

If, therefore, we wish to find the thickness of ice which will 
just be sufficient not to induce melting at the bottom, we must 
put 32 for a; and if, with Dr. Croll, we suppose the mean 
temperature of the surface exposed to the air to be 0° F., we 
must put 0 for 6. Whence 


= == 4UbLS 
e 


-e— (45 teeth. 


If the thickness of the ice be less than this, no melting will 
take place ; but if greater, there will be melting at the junction 
of the ice and rock. 

Here no account has been taken of the lowering of the 
melting-point by pressure. But that is easily allowed for. 
For, comparing the height of a column of ice whose pressure 
is equivalent to a column of mercury of 30 inches (or one 
atmosphere), it is 37 feet. | 

Since, then, the melting-temperature is lowered by 0°0137° F. 


ia ot re eee, Te 


on the Stratification of the Antarctic Ice. 385 


for each additional atmosphere of pressure, it will be lowered 


= x ‘0137° for the thickness e of ice. 


Hence we shall have, to determine the limiting thickness of 
the ice at which its lower surface will begin to liquefy, 


é 
x 04441; 


: “, e=/14 feet. 


(2) No certain limit can be imposed upon the thickness to 
which the ice might accumulate, provided the snowfall be more 
than sufficient to counterbalance the melting at the bottom. - 

We have found the critical value of the thickness of the ice so 
that melting should just not take place. Suppose the ice thicker 
than this; then the bottom of it will begin to melt, and con- 
sequently must be at the melting-temperature corresponding — 
to the pressure. The flow of heat out of the earth will melt 
off a layer of it annually. But the whole of this flow of heat 
will not be so employed, because, the ice being maintained 
_In a condition in which its upper and lower surfaces are at 
different temperatures, there must ensue a flow of heat through 
it. This flow of heat will be expressed by the equation 


— 


Or if, as before, we assume the temperature of the upper sur- 
face of the ice to be zero, and allow for the lowering of the 
melting-point by pressure, 


pap o2 eX 00087 


€ 

Now it is obvious that there is no source from which this 

flow can be derived, except the flow out of the earth. Hence 

F’, which is the flow out of the earth, must be split up into two 

portions, F—fand f/f; of which F—/ goes to melt the ice at 

the bottom, while fis conducted away through the ice into 
space beyond. Now 


fak 


Oenb. 
e 


32—e x 000387 


We see, then, that as the thickness of the ice is increased, f ts 
diminished, and the less heat escapes through the ice; and 


386 Mr. O. Fisher on the Thermal Conditions and 


when the thickness exceeds sixteen miles none will escape. 
But if none escaped, so that the whole of F was employed in 
melting the ice, Sir William Thomson asserts that it could 
only melt one fifth of an inch annually at the ordinary tem- 
perature and pressure. If, therefore, the snow-fall considerably 
exceeds this small amount, there seems to be no reason why 
the ice might not accumulate to a much greater thickness than 
the above, as far as melting at the bottom is concerned. 

Note.—Professor Everett says, p.45, that Sir Wm. Thomson’s 
results are given in terms of the foot and second, and that 
consequently they have been multiplied by 929 to reduce them 
to the C.G.8. system. Hence to bring back K and &, as given 
by Professor Everett, to the system of units used here, we 
must put 


"00581 
ae 929 
and 
re 00218. 
I NEGZO 


The thermometric scale used does not affect the value of the 
conductivity. 

The next question which we will attempt to answer regards 

(3) The mode of origin of the stratification of the great tabu- 
lar icebergs of the south. 

Supposing that each separate stratum, distinguished by 
alternations of more or less clear ice, is the product of the 
snowfall of a single year, Sir Wyville Thomson suggests the 
following as the mode by which the lower strata may have 
lost some of their original thickness:—“ It is probable that, 
under the pressure to which the body of ice is subjected, a 
constant system of melting and regelation may be taking place, 
the water passing down by gravitation from layer to layer 
until it reaches the floor of the ice-sheet, and, finally, working 
out channels for itself between the ice and the land, whether 
the latter be subaerial or submerged.” 

Is this process of melting and regelation possible? If we 
consider the ice-sheet uniform in structure and at rest, it is 
obvious that the pressure upon any given area of section will 
be greatest at the bottom, where also the temperature will be 
highest. Consequently, under these circumstances, the bot- 
tom is the only place where the pressure would induce melting. 
But it may be replied that the ice is not at rest, but is moving 
outwards towards its free edge. And pressures in the hori- 
zontal direction may be connected with this movement greater 
than the vertical pressures due to the mere depth. It must, 


on the Stratijication of the Antarctic Ice. 387 


however, be recollected that the outward movement of the ice 
is not caused entirely by a horizontal pressure arising from a 
vis a tergo, but that at every place there is a tendency to flow 
outwards towards the unsupported free edge. In ordinary 
glaciers the strain thus produced occasionally gives rise to 
crevasses. It seems improbable, therefore, that the horizontal 
pressure should ever exceed the vertical; so that if the latter 
cannot induce melting, neither can the former do so. 

It is, however, more likely that what Sir Wyville Thomson 
contemplated was that the pressure of one layer upon the next 
is not evenly distributed, owing to the layers being in contact 
in some places but not in others. In this case the pressures 
upon the areas in contact might increase to a great amount, 
provided the areas of contact were sufficiently small. And it 
is quite likely to be partly in this way that névé is converted 
into solid ice; for the contact along any horizontal plane is 
confined to those areas in the névé which are occupied by ice 
and not by air, so that the pressure on these surfaces is much 
greater than if the ice were uniformly solid. In fact, the mean 
pressure upon the portion of any area which is occupied by 
ice is to the pressure due to the depth alone as the whole of 
that area is to the area occupied by ice. When the conversion 
of névé into ice has taken place, it is not easy to understand 
how the process of melting and regelation can go further. 

But Dr. Croll has pointed out that the diminution of the 
thickness of the annual strata of ice from the top downwards 
may be accounted for by the fact that the ice radiates from a 
centre of dispersion. Although I am fully aware of the very 
slight practical value of any addition I can make to what Dr. 
Croll has said upon this part of the subject (for we are too 
ignorant of the physical properties of ice to arrive at any cer- 
tain results), I propose nevertheless to offer a few further 
remarks upon the mode of origination of the stratified structure, 
and the consequences which follow as affecting the thickness 
of the strata. 

The snowfall of each year is deposited upon that of the pre- 
vious year; and there is no internal cause to alter this order of 
“conformable” arrangement of the strata. It is conceivable 
that the movement of the ice over a rough rocky surface might 
dislocate the strata, or that the liquefaction of the upper surface 
over partial areas might cause the snowfall of certain periods 
to be removed before the deposition of some later strata took 
place, and so render the strata unconformable. But these dis- 
turbing causes are supposed not to be present. It follows that, 
in any vertical column, the snowfall of every year intermediate 
between the earliest represented in it (which will be at the 


388 Mr. O. Fisher on the Thermal Conditions and 


bottom) and the most recent (which will be at the top) must 
have its corresponding layer. 

Joining the corresponding layers in contiguous columns, it 
appears that there must be a regular stratification, as was ob- 
served to be the case, and that the strata will not deviate far 


from horizontality. The question then arises, Where were 


these strata deposited ? and what regulates their thickness ? 
| ‘Fig. 1. 


B oO 


Let a cylindrical surface AB be described in the ice-cap 
around the polar axis P O, with radius 7 approximately equal 
to PA. Also describe a ring on the surface of the ice, whose 
width is w,; and let p, be the distance of the edge of it further 
from the pole. N M isa section of this ring, and P N=p, ; 
N M=w,. : 

Now, if the form of the ice-cap is permanent, the snow which 
falls upon the ring, and upon any part of it, will always follow 
the same route to meet the cylindrical surface at AB. Sup- 
yose N K to be the route taken by the particles which travel 
from N, and ML by those from M. It is evident, then, that 
the ice at A B will consist of layers, each of which is continu- 
ally fed by the snowfall upon its own corresponding ring 
fixed in position upon the surface, and that the rings nearer 
the pole will supply the lower layers. This conclusion is in- 
dependent of any assumption as to the forms of the paths 
pursued by the ice. It only supposes that these paths do not 
cross one another. : 

Suppose that AB=A, KL=6h,. Then, if s be the depth of 
the annual snowfall upon N M, we must have the quantity of 
ice which passes outwards each year through the cylindrical 
surface at K L equal to the annual snowfall on the ring at N M. 

Now the area of the ring at N M is 


7(Px —(p,— w,)) = T(2puWn —w?). 


Taking v to represent the mean annual velocity through K L 
per annum, we must have, from the above consideration, 


on the Stratification of the Antarctic Ice. — 3889 


2rrvoh, =7s(2p,w, —w2)- 


2 


S Wn 
6h, = aye (pate 9 ° 


This relation expresses the thickness of the layer of ice at A B 
which is derived from the snowfall on the ring whose section 
is NM. 

If, then, 5h, be the thickness of a layer derived from one 
year’s snowfall, or an annual stratum of ice at A B, this im- 
plies that it takes one year more for a particle to travel from 
M to L than from N to K. 

(4) To account for the downward diminution in thickness of 
the annual strata of ice. 

For the width of the ring next nearer to the pole we shall 
have to substitute for p, the value p,—w, ; and if the width of 
that ring be w,+«, and 6h,_, the thickness of the correspond- 
ing stratum at A B, taking s and v as constant for adjoining 
_ strata, we shall have 


n= 2 ((p,—w,)(wo, +a) — “AF2L), 


whence it appears that 
eG Gg? 
Bin Sin i= 2 (wt + & —a(p,—2,)). «+ (A) 


Now we do not know whether the rings which contribute 
the annual strata diminish or increase in width as they ap- 
proach the pole. But we may gain a knowledge of the effect 
which a diminution or increase in the width of the rings would 
have upon the relative thickness of the successive strata at 
A B by putting 6h, —6h,_, =, and considering it as the ordi- 
nate of a curve whose abscissa is a. If we suppose A B to be 
near the free edge of the ice-cap, r will be large; and we may 
without much risk of error consider v constant for all depths 
above the water-level in that position. 

Substituting 8 and suppressing the suffixes, and writing m 


Ce 7 side 
for fe) which we now take as constant, and observe that it is 


large, because although v is small, yet vr is large and s is 
small, we obtain 


(a —(p 20)? =2m (2 a eae) 


This represents a parabola whose axis is vertical, and which 


390 Mr. O. Fisher on the Thermal Conditions and 
has for the coordinates of its vertex, 


‘a _ pee y 
p—2w and ae 


The latus rectum ae is Independent of p and w, and may 


be taken as constant. Supposing that we draw the curve with 
assigned values of p and w, then the ordinate @ to abscissa a 
will give the difference in thickness between the strata at A B 
which are derived from two contiguous rings whose widths 
are wand w+a. 


2 
If we put a=0, then B= = ; so that the height at which 


the curve cuts the axis of @ is independent of p, except so far 
as w depends upon p. ‘The points at which the curve cuts the 
axis of a are given by the relation 


“a=p—2w+/(p—2w)y’—2w’. 


This must be always positive. 
Taking the smaller value, and observing that, except near 
the pole, p—2w is much greater than w, we have, expanding, 

ne 

w 


os nearly, 


p—2w 
which, except near the pole, is much smaller than w. As 
soon as « exceeds this value, 6 will become negative. 
The greatest negative value of 6 will be attained at the 
vertex, where 
a= p—2w. 


In this case it will be found, by reference to the distances 
measured from the pole, that this value of « would carry the 
ring whose width is w+ up to the pole itself. 

We can now perceive in a general way how a decrease or 
an increase in the width of the rings as they approach the pole 
would affect the difference in the thickness of successive strata 
at A B. 

The latus rectum of the parabola being constant, the curve 
always maintains the same size. We have therefore only to 
draw it with its axis vertical, and to place the vertex in the 
position corresponding to the assumed values of p and w. It 


2 
will then necessarily cut the axis of 6 at the height = above 


the origin; for this is the value of the ordinate corresponding 
toa=0. This shows that, if the rings were of uniform width, 
the difference in thickness of the annual strata at A B would 


on the Stratification of the Antarctic Ice. 391 


be constant ; or, in other words, their thicknesses: would form 
a decreasing arithmetical progression, whose common differ- 


w 
ence would be pe 


Let curve 1 in fig. 2 be drawn with any assumed values 
Fig. 2. 


of panda. And, first, suppose the rings to decrease in width 
as they approach the pole. Then the difference in thickness 
between the ring under consideration and the next nearer to 
the pole is given by the ordinate corresponding to the assumed 
value of a on the left of the origin. We observe these ordi- 
nates to be all positive. Hence the strata decrease in thick- 
ness. 

Now take other values of p and w nearer tothe pole. Then 
both p and w will be diminished. On account of the diminu- 
tion of p, which we suppose much greater than w, the vertex 


of the parabola will be raised ; and because = is diminished, 


the point at which it cuts the axis of 6 will be lowered (com- 
pare curves 1 and 2), and the ordinate corresponding to 
the former negative value of « will be less than it was before, 
and less still for the probably smaller value of « which corre- 
sponds to the diminished value of p. Hence the difference in 
the thickness of the strata will become less and less for the 
lower ones. 

Next suppose the width of the rings which supply the an- 
nual strata at AB to increase as they approach the pole. 
Then the difference in thickness between the stratum derived 
from the ring under consideration and the next to it nearer 
to the pole is given by the ordinate corresponding to the 


392 On the Stratification of the Antarctic Ice. | 
assumed value of & on the right of the origin, and, as before, is 
2 

positive unless is greater than ae 

Now take other values of p and w nearer to the pole. Then 
p is diminished, while w is increased. On account of the di- 
minution of p and increase of w, the vertex of the parabola 
will be brought nearer to the origin, and raised (but more so 
than in the previous case, when the rings diminished). And 


2 
because = is increased, the point at which the curve cuts the 


axis of B will be raised (compare curves 1 and 3), and the or- 
dinate corresponding to the former positive value of « will be 
greater than it was before ; and for a slightly greater value of 
a, such as we may presume belongs to the next pair of annual 
rings towards the pole, it will be still greater ; and so on for 
the next position of the curve. Consequently in this case the 
difference between the thicknesses of the annual strata will 
for large values of p be at first small, and will become larger 
in descending. But should the value of & increase rapidly, as 
it may possibly do on approaching the pole, then the difference 
would begin to decrease. 

But the strata which are visible above the water-level must 
certainly be derived from rings distant from the pole, for 
which the values of pare large. Hence, on the whole, we may 
conclude that in the visible ice-cliff the differences of thick- 
ness in the strata in descending (1) would be constant if 
the rings from which they are derived were of uniform width, 
(2) the difference would diminish if the rings diminished in 
width, and (3) it would increase if they increased in width. 

It does not appear that any sufficiently close observations 
have been, or perhaps could be, made to determine the rate of 
decrease in the thickness of the successive strata. In the ad- 
dress referred to, Sir Wyville Thomson tells us that the ice- 
cliff of a berg was on an average about 200 feet high, that 
at about 80 feet below the top the strata were about a foot 
thick, and near the water-line about three inches. These data 
are not sufficient to warrant any conclusion beyond the mere 
fact of the diminution in thickness. 

Let the points 7 and g be so taken, in fig. 1, that the time 
which a particle of ice takes to travel from N to K is equal to 
that which it takes a particle to travel from vr to L; and simi- 
larly from M to L and from q to R; then, if NM and MQ 
supply annual strata at A B, it will take one year for a particle 
to travel from M to 7, and the same period for one to travel 
from to g. Hence the mean velocity through Mv : mean 
velocity through Qg:: Mr: Qg. 


On the Action of Light upon the Soluble Iodides. ~ 308 


But it may be fairly assumed that M » is greater or less than 
Q q, according as N M is greater or less than MQ. Conse- 
quently, if the rings supplying the annual strata increase in 
width, the velocity of the ice near the surface also increases, 
as the pole is approached, and vice versd. 

The permanence of height in the ice-cap must depend upon 
the fact, that the resolved part of the annual velocity near the 
surface in the vertical direction is equal to the depth of the 
annual snowfall. Consequently, for a given path, a widening 
of the rings corresponding to a greater velocity would be 
consonant with a thinner ice-cap, and a narrowing of them 
with a thicker one. 


LXII. Action of Light upon the Soluble Iodides, with the Out- 
lines of a New Method in Actinometry. By Apert R. 
Lreps, Ph.D.* 


eee question as to whether potassium iodide, in dilute so- 

lution, is decomposed by free sulphuric acid, has fre- 
quently been made a matter of controversy. Schénbein 
contended that it was not, and, in an acrimonious reply to Prof. 
Fischer (Journ. fiir prakt. Chem. 1845, xxxiv. p. 492), im- 
pugned the purity of the latter’s chemicals. The same ground 
was taken by Houzeau, in a discussion with M. L. Sauvage 
(Comptes Rendus, 1868, Ixvii. pp. 633, 714, 1138), the former 
going so far as to state that, when the solutions were a thou- 
sand times dilute, no decomposition took place even on pro- 
tracted boiling. These discrepancies appear to have originated 
from an oversight of the essential part played by air or oxygen 
in the reaction. This is represented by the general equation 
MI+HA+0=MA+H,0 +I1,where M indicates the basic and 
A the acid radical, coefficients being omitted. This holds true 
not only of the ordinary mineral acids, but has been verified 
in the three of the organic acids experimented upon—oxalic, 
tartaric, and acetic acids. In the dark the decomposition di- 
minishes with the increase of dilution, being indeterminable, 
when the dilution has reached the one-thousandth, at the end 
of twelve hours, but plainly recognizable when the dilution 
has attained the one four-thousandth at the expiration of five 
days. ‘These figures apply more especially to the potassium- 
iodide and sulphuric-acid solutions, upon which very nume- 
rous quantitative determinations of the liberated iodine were 
made. In sunlight the amount of iodine set free increases in 
the same ratio as the increase in surface of exposure to the 


* Communicated by the Author. 


394 Dr. A. R. Leeds on the Action of Light 


sun’s rays, or, in case of solutions exposed in tubes of colour- 
less glass and of uniform bore, in the same ratio as the increase 
of volume, or the dilution. In the absence of air, no decom- 
position takes place either in light or darkness. When the air 
has been entirely removed by a long-continued current of car- 
bonic acid, the solution may be exposed for days to the sun 
without undergoing change. If the carbonic acid be replaced 
by a stream of oxygen, decomposition begins, and, in the case of 
potassium-iodide solution a thousand times dilute and exposed 
to the sun, may attain to 6 mgrms. of liberated. iodine per 
hour. 3 

When these principles had been experimentally established, 
they were applied in the first instance to an actinometric 
measurement of the solar ray. The solutions were contained 
in comparison-tubes, which when filled to the depth of 150 
millims. held 100 cubic centims. In each were placed 1 cubic 
centim. of potassium iodide of 10 per cent., 1 cubic centim, of 
sulphuric acid, 5 cubic centims. of starch-water, and sufficient 
water to make up the volume to 20, 40, 60, 80, or 100 cubic 
centims. They were supported on a frame kept normal to 
the sun’s ray. The results are summarized in the accom- 
panying diagram ; and it will be noted that the curves of the 
more concentrated are regularly circumscribed by those cor- 
responding to the more dilute solutions. The determination 
was interrupted at 2 p.m. by the sun’s clouding over; but when 
resumed two days later, numbers were obtained which intro- 
duce no sudden breaks in their appropriate curves. 

Tn the subsequent experiments the acids employed were some 
_prepared with especial care by myself, and of such strength 
that 1 cubic centim. of the sulphuric was equivalent to 25 
cubic centims. of a normal soda solution, 1 cubic centim. of the 
hydrochloric to 10°7 cubic centims., and 1 cubic centim. of the 
nitric acid to 12°6 cubic centims. of the normal soda. Similar 
remarks apply to the soluble iodides, of which 1 cubic centim. 
of a 20-per-cent. potassium-iodide solution was used in each 
of the subsequent trials, and 1 cubic centim. of solution of the 
remaining iodides, these solutions being chemically equivalent 
to a 10-per-cent. solution of the potassium iodide. In every 
ease 1 cubic centim. of the acid was likewise employed, and 
the liquid made up to 100 cubic centims. Advantage was 
taken of an exceptionally brilliant day; and the actinometric 
measurement was repeated with the above reagents, the results 
being as given in the subjoined Table (p. 396). The figures in 
the vertical columns are milligrammes of iodine set free du- 
ring each half hour of the day. It having been found that the 
amounts of iodine set free in the absence of starch much ex- 


HOURS OF THE DAY. 


ers 
ct 
CO 
—_ 
<= 
N 
re} 
a 
rs - Es 
ib) 
2a | 
a Ss 
mel 
x 8 
ee 
Sos 
oS = 
—, 
> es 
ge 
Shee 
Se oe 
= 
5 
oD) 
ent 
i) 
| 
) 
om 
ae) 
a 


“ANIGOI JO SANNVASDITTIINILNGD 


396 Dr. A. R. Leeds on the Action of Light 


Actinometric Determinations, February 27, 1879. 


9 a.m.—| 9.80-| 10- |10.30-| 11- | 11.80-] 12- 12.30- 


pepeenis, 9.30. | 10. 10.30.) 11. |11,30.| 12 m. |12.80.| 1 par. 

loc. H,80,+1 ce. K1....... 215 | 250 | 285 | 290 | 280 | 285 | 270 | 2-90 _ 
Weta os. 1-00 | 1-15 | 1-25 |.1-40 | 1-70 | 1-70 | 155 | 1-65 
lc. H,80,+1 ec. Cal, ..., 115 | 130 | 45 | 1-55 | 1-70 | 165 | 1-70 | 1-95 
. Claes ]0-75 | 085 | 1-00 | 1-00 | 1-05 | 1-20 | 1-40 | 1-40 

lec H,80,+1 c0. Lil..,...| 1-20°1 1-30 1135 | 1-45 |eoneOe een Lz | 

Necross 0-75 | 0:80 | 0:95 | 1-00 | 1-00 | 1-00 | 1-10 | 1-20 
1 cc. H,80,+1 oc. NH,L...| 130 | 1-40 | 155 | 165 | 1-80 | 1-70 | 1-80 | 1-90 
eae “") 085 |0-95 | 1-00 | 1-05 | 115 | 115 | 1-45 | 1-20 

Reagents. -—/1+1.30./1.30-2.2-2,0,|2.30-3./3-8.30.|8.80—4./4-4.30.4.30-5., 

Loc. H,80,+1 ce. KI ......| 3:25-| 300 | 250 | 295 | 2000 IeyaInOnemiD-o5 
. Hol... 200 | 1-70 | 1-60 | 1-45 | 1-25 |0-90 | 0-35 | 0-23 
1 cc. H,80,+1 cc. Cdl, ...| 220 | 1-95 | 1-70 | 1-50 | 1:30 | 1-10 | 0-70 | 0-43 
Oe 7c Aen need 150 | 1-50 | 1-20 | 0-95 | 0-90 | 0:65 | 035 | 0-20 


1:55 | 145 |) 150 | 140 |-i:25" pbs OGa |) 0-43 
1-20 | 1:10 | 1:00 | 0°75 | 0-70 | 0:50 | 0:30 | 0-18 


1 ec. H,80,+1 ec. lil ...... 
HCl 


9 GF ee wee ieiere)s 


195 | 180 | 1-70 | 150 | 120 | 1-05 | ovo | 0-45. 
115 | 115 | 110 | 085 | 0-90 | 060 | 0-30 | 0-18 


lec. H,80,+1 cc. NH, ... 
H 


39 BG ee teleiedeves: 


ceeded those liberated when starch was present, these results, 
unlike those represented in the preceding diagram, were ob- 
tained with acid and iodide only, and are correspondingly 
greater throughout. The ratio of the iodine liberated in the 
potassium-iodide solution with sulphuric acid is to that libe- 
rated with hydrochloric acid as 2°33 : 1:31, in the cadmium- 
iodide as 1°47 : 1:0, in the lithium-iodide as 1°31 : 0°85, and 
in the ammonium-iodide as 1:47: 0°92. ‘The above results 
are graphically represented for two of the curves in the ac- 
companying diagram. : | 
An actinometric measurement was then made of the electric 
_ light, similar solutions being employed. A cylindrical stand 
was used, of such dimensions that the centre of the axis of the 
100-cubic-centims. column contained in each comparison-tube 
should be at a distance of 6 inches from the focus of the elec- 
tric light. The electric arc was taken between carbon points, 
and was produced by electricity generated with a dynamo- 
electric machine run by steam-power, its illuminating capacity 
varying during the course of the experiment, according to 


upon the Soluble Lodides. 397 


photometric measurements made by Professor Morton, be- 
tween 7000 and 7500 candles. 


=I 
Z 
_— 
i=) 
=) 
= 
= 
co) 
m 
= 
= 
= 
< 
ra 
o 
= 
+e) 
=| 
— 
= 
— 
> 
ze 
e 
oO 


HOURS OF THE DAY. 


Phil. Mag. 8. 5. Vol. 7. No. 45. June 1879. 


398 Dr. A. R. Leeds on the Action of Light 
Hlectric Light. fe 


20 minutes. 7% minutes. 
lee. H,SO,+1ec. KI =3°90mgrms.I. =3: 00 meriate! des. 
os eT - =o 9% =200° 

= 3°40 a — | 
Le. H, 80, 4-1 cc. Cdl, ==3:15 a = 2a oe 
> Bl 5 = 2°30 be == Fao tee 
eee, ” = 2°50 ” Ree | 
lec. H,8O,+1¢.c. Lil =8-00 ee =2- 1 
sy: oe = bo be == 00s = 
Lee. H, S80, +tee NE, 5-2-5080 _ = 20 
5 ELeH = ==°D0 - = DSBs 
oo eI ” =1°385 ” oh. 


The reason for the variation in the two experiments is not 
quite clear; for while the light was remarkably uniform du- 
ring the second experiment, there was no such striking differ- 
ence in the apparent luminous effect. 


Magnesium Light. 


E. Il. (1 hour), III. G hour). 
| merm. I. merm. I. megrm. I. 
lec. H, SO,+1 ¢.c. KI lost =0:050 =0°015 
ae =0'225 =0075  =0-050 
” Fi SO, + if C.Cc. Cdl, = = 080 = 0°035 =0:010 
53. EEO = 07950) =O ae =(-a0 
5 H,SO,+ lec Lil =0:075 =0-040 indet. 
55 eel =()165, . =0:050 = 0-060 
” H, SO, = ea Cc. NH, I ==Q7 EES = 0:060 = 
a ERE a = O200:: 0,076 — 


The light was furnished by a single-ribbon magnesium 
lamp, run by clockwork. The reason for repeating the expe- 
riment three times was that the ratio of decomposition in pre- 
sence of free hydrochloric acid was greater than in presence 
of free sulphuric acid. When the sun and electric light were 
employed, it was always less, the reagents being of the 
strengths above given. It will be necessary to determine the 
rate of decomposition in each case, for the various regions of 
the spectra of the three lights, before venturing upon an ex- 
planation of these differences. 

The foregoing results are brought together in the following 
Table, and likewise illustrated in the diagram. ‘The numbers 
found for the magnesium light have been multiplied by ten, 
in order to bring the corresponding curve into the same illus- 
tration with the others. 


IH Z+HYHNZ 


hos “as? HNZ 


| 19H@ 4197 


Ek 


—|*O ¢*H +11T? 


-| LOH e+ TPO 


+0 9°%H+7IP) 


upon the Soluble Lodides. 


LOH Z+1 UZ 


a 
te 


+oStHius 


“ONIGOI JO SUNNVASITIIN 


400 = On the Action of Light upon the Soluble Todides. 


Decomposition during equal times (1 hour). 


Electric light. Sun. Magnesium. 
H,S0O,+ KI =19°5 mgrms.I. 6:5 mgrms.I. 0°05 mgr. I. 
H a AnQ.tner 1A 0-075 ,, 
H; SO, + Cdl, — 14°6 ” AA. ” 0°035 ” 
ree = 8-8 ee 0-050, 
lee SO,+4+ Lil == |) 327) ” 3:1 ” 0:04 ” 
Mele. = 65a ee 0:05 ,, 
H,S0,+NH,1=150 5 = 39. st 0:06, 
HO 3 EOS ere a 8 O07 568 


As yet no actinometric measurements of spectra have been 
made by this method. As a preliminary determination, how- 
ever, the amount of action upon the soluble iodides, after the 
light of the sun and electric arc have traversed certain ab- 
sorbing media, has been studied. The comparison-tubes were 
supported in the centres of tall wide-mouth bottles, so as to be 
surrounded by an equal thickness (3 centims.) of the absorb- 
ing medium on every side. Their tops and those of the bottles 
were closed in with tinfoil, so as entirely to prevent access of 
light, but admit air. The blue medium was ammoniacal solu- 
tion of copper ; the yellow, neutral potassium chromate ; the 
red, fuchsine. Their strength was adjusted to the point of 
equal translucency. 


Absorbing Media (time 1 hour). 
Sunlight. Electric light. — 
megrms. I. megrms, I. 


tees 1 cc. Hy SO,+1 eel + = 255 = 6:00 
» HCl ” =2°22 =4:50 

Yellow 1 ec. H,S0, +1 cc KL  =O67 —():50 
a » HCl ” =0°45 =(0°45 
Red 1 cc. H, O,+1 ee Ki =a — 4:95 
ca yy HCl ” = 0°83 = 3:00 


While in the preceding experiments the action in the elec- 
tric light has been approximately the maximum of that occur- 
ring in sunlight, this ratio, when absorbing media were used, 
was approached only in case of the blue and red solutions. In 
other words, the yellow medium absorbed a much larger rela- 
tive proportion of the actinic rays of the electric light than of 
those of the sun. 


Stevens Institute of Technology, 
Hoboken, N.J., April 15, 1879. 


EL. 400- (J 


LXIII. A new Theory of Terrestrial Magnetism. 
By Professors JoHN Perry and W. H. Ayrton*. 


. the autumn of 1876, while experimenting on magnetic 
transparency, we designed an apparatus for testing whether 
a moving body having a definite electric charge would, like a 


current, deflect a magnet. While waiting for the conclusion 


of the rains, and the advent of the very dry season which ac- 
companies a Japanese winter, in order to try our instrument 
in conjunction with an ordinary plate-glass electrical machine, 
we received the account, published in the Philosophical Maga- 
zine for September 1876, of the experiments just performed 
by Mr. Rowland in the laboratory of Professor Helmholtz, 
by which it had been conclusively shown that a charge of 
electricity mechanically moved had the properties of an ordi- 
nary electric current as far as the deflection of a magnet was 
concernedf. 

Until this point was settled, it was unlikely that attention 
would be directed to the electromagnetic effects that might 
arise from the rotation of a charged body like the earth. 
Shortly, however, after the execution of the experiments re- 
ferred to we attempted (as described in our paper “ On Rain 
Clouds and Atmospheric Hlecitricity,’’ which appeared in the 
Philosophical Magazine for March 1878) the solution of a new 
theory of terrestrial magnetism. This problem we have 
attacked in a variety of ways ; and the following solution, to 
which we have at length been led, we beg to offer for the ac- 
ceptance of the Physical Society. 

The points near the surface of the earth have different linear 
velocities from those in the interior (although all the points 
have the same angular velocity of rotation round the earth’s 
axis) ; therefore, if the earth had an initial electrical charge, 
residing of course, in accordance with the well-known electrical 
law, on its surface, the electrified particles would have veloci- 
ties relative to the remainder ; hence, as a direct consequence 
of the results of the experiments published by Professor Helm- 
holtz, the interior of the earth would be a magnetic field, quite 


* Communicated by the Physical Society, having been read at the 
Meeting on March 8. 

7 Additional confirmation has recently been given on this subject by 
the experiments described by Mr. Crookes in his paper on the “ Illumina- 
tion of the Lines of Molecular Pressure &c.,” since he has shown that the 
stream of particles which is shot off from the negative terminal in a very 
perfect vacuum, and which produces the green phosphorescence, carries 
electricity with it and is deflected by a magnet. This may be regarded 
as a sort of converse experiment, since it proves that a magnet deflects a 
moving charge of electricity. . . 


402 Professors Perry and Ayrton on a oe 


independently of its interior constitution. And precisely similar 
reasoning, of course, proves that outside the earth’s surface 
there would also be a magnetic field. (Vide addition at the 
end of the paper.) To determine the strength of this field we 
have the following relationship to start with, 

In § 526, Clerk Maxwell’s ‘ Electricity,’ it is shown that 
an element of current C, of length ST, acts upon a unit mag- 
netic pole at a point P with a force 


ca, sin PST, 


in a direction at right angles to PS and ST. Combining this 
with the experiments referred to above, we may assume that 
if a charge of static electricity (measured in electromagnetic 
units) Q, at the point 8, moves in a direction ST with a velo- 
city v relative to a point P, it produces on a unit magnetic 
pole at P a force 


=~ sin PST, 

in a direction at right angles to PS and ST; and this is the 
only assumption employed in the following investigation. 
Now suppose the earth to have the uniform density of elec- 


tricity o over its surface, and let its radius be unity. Consider. 


the force produced, by the rotation of the electricity at a point 
S on the surface having coordinates 7, 0, 6, at a point inside 
the sphere having the coordinates 7, 6, ¢;. Then if the 

sphere be rotating with an angular velocity w round the axis 
of z, and if @ be the angle between this axis and a radius, 
while @ is the angle between the axis of w and the projection 
of a radius, the velocity of S relative to P will have for its 
coordinates 


u or —w (sin sin ¢@—r sin O; sin ¢;) parallel to 2, 
tor w/(sin 0cosd—rsin 6, cos ¢) parallel to y ; 
also 
PSY=?+m?+n’, 
where 
[= sin @ cos —7 sin 0; cos gy, 


m= sin #sin é—7 sin 6, sin gy, 
n= cos 0—r cos 0}. 


Now the direction-cosines of PS are proportional to J, m, and 
n; and the direction-cosines of ST, the direction of mono of 
S relatively to P, are proportional to u, v, or to —wm, wi, 
and 0. Consequently PS is perpendicular to ST. Also, if A, 


a i i 


T ane of Terrestrial Magnetism. 403 


#, v are the direction-cosines of a line at right angles to PS 
and ST, 


Be nl 
PSV P+ mi 
mn 

PSY? +m 

—(m ne) 
~ PSS P+? P+ m 
where the negative sign must be given to the root. Now if 
F is the force at P due to the charge of surface-density o on 
the elementary area d@.sin @.dd at S moving relatively to P, 


we know that it must be at right angles to PS and ST, and 
equal to 


b= 


osin@.d0.déx sin PST Vv? + #. 
PS 
Hence, if 6X, SY, 6Z be the resolved portions of the force F 
parallel to the axes of coordinates, and if dS stands for 
sin 0.d@.dq¢, we have 
sy — Ged . Sut! +t?) 
PS 


and similarly for SY, 6Z. 
Hence, if sj stands for the summation over the whole sur- 


face of the sphere, and if X is the total force at P in the direc- 
tion of the axis of «, 


— nb : 
PY PSY? +m? 
cwds | Ee 2. 

PS?- 
owdS m 
PSY “PS 


owds m7+P n 
PS? n PS 


Now the resolved part of the force along the axis of xis the 
same as would be the force in that direction due to a distribu- 
tion of attracting matter of density —now over the surface of 
the sphere. Similarly the resolved part of the force along the 
axis of y is the same as would be the force in that direction 
due to a distribution of attracting matter of density —now over 


oo 


404 Professors Perry and Ayrton on a new 


the surface of the sphere ; and the force in the direction z is 
the same as would be the force in the same direction due to a 


2 2 2 
distribution having a density ow cea or ow (= - n) 


n 
Regarding the force as being due to such a distribution, 
= ee own dS 1 
ie PS? Va eats PS?) Vis 


Now the first integral is (\5, which we know has a 


value equal to the potential inside the sphere due to a uniform 
distribution of density ow over the surface, and is therefore a 
constant, 47raw. So that the entire force in the direction z is 
47row minus the force in direction z due to a distribution of at- 
tracting matter of density now over the surface of the sphere. 

Now it is easy to show that a distribution of attracting 
matter of a density proportional to n or to A+Ccos@ over 
the surface of a sphere will give 


X= 0; 
Y=0, 
Z= a constant ; 


therefore all that is necessary is to determine the value of this 
constant. We neglect the term A, because a uniform distri- 
bution produces a constant potential, or a zero force in all 
directions; the distribution Ccos@ being a zonal harmonic, 
produces a potential inside the earth, 

Y= an r cos 0,, 


a 
Aq 
= Ce; 


so that the force Z which equals is a Thus for the 


distribution C cos @ we have the force =e C; so that the con- 


stant force above mentioned, 47raw, requires the distribution 
30w cos @. From this we must subtract the distribution now, 
or ow (cos 9—r cos 6,), giving us for the total distribution of 
attracting matter over the surface of the sphere a density 


2ow cos 9+ awr cos I; ; 


but the latter term means a uniform distribution, producing 
therefore no internal force, and may therefore be neglected. 
And the first term is a zonal spherical surface harmonic; there- 


ee 


see ee eee 


Theory of Terrestrial Magnetism. 405 


fore the electromagnetic potential due to the fone of the 
electricity on the surface of the earth is 


a 2owr cos 6, Taras the earth, 


and 


= Q2ow 5 cos 6, outside the earth, 


where w is the angular velocity of the earth on its axis, r the 
radial distance of any point from the earth’s centre, @, the co- 
latitude of the place, 47a the total quantity of electricity uni- 
formly distributed over the surface of the earth measured elec- 
tromagnetically, and the unit of length the earth’s radius. 


These results, which we think are logical consequences of 
the experiment performed in Professor Helmholtz’s laboratory, 
and referred to at the commencement of this paper, may now 
be applied in various ways. 

For example, if the iron of the earth is arranged nearly in 
a hollow sphere, of external and internal radius a, and a, 
then, since the potential given above is a zonal harmonic, 
we can at once apply Poisson’s result; and we find that the 
potential due to magnetization of the hollow sphere is 


Sir 
Sa ae 
4rx(3 + 87rKk)(a3—a?) ees to 
9+ 367K + 327°«"(a3—a3) x? 
for all points outside the outer surface of the sphere; and 


hence, for points outside the surface of the earth, the total 
magnetic potential is 


Le war 


: 
ae ee FA ae a) 3 4 cos 6 
L904 86re+Blae(a—a) * 8 | Pr? 


, 
where « is the coefficient of ec. 

Now Biot’s approximation to the law of intensity of the 
force is 

—/143 sin? A, 

where J is the latitude of the place; and we understand that 
this approximation is generally considered, for rough purposes, 
as a fairly accurate one. 


Our equation for any point at a distance r from the centre 
and having a colatitude @ is 


cos 8 
V=M Sgt 


406 Professors Perry and Ayrton on a new 


— S is the force directed towards the north, 


_ _ is the force directed downwards tomande the earth’s 
‘i centre ; 
therefore, if I be the magnetic intensity, 


2 2 
A (=) 4 = 


dé ar 
M’sin?@ 4M?’ cos?@ 
aR arene oh? cea 


or, putting r equal to unity (that is, for a point on the earth’s 
surface), 


I=M\/1+3 cos? 6 © 
=M/1+4+8sin?A, 


which is Biot’s expression. 

Now this is a result which could not have been anticipated, 
and speaks well for our new theory of terrestrial magnetism. 

It is well known that many forms of distribution of iron 
inside the earth may be found which, with the existing poten- 
tial given above, will produce Gauss’s distribution of potential 
over the surface of the earth ; and it would be very interesting 
to try how close an approximation to the real potential would 
be obtained by considering the iron of the earth to form a 
hollow ellipsoid, one of its principal axes coinciding nearly, 
but not quite, with the earth’s axis. This calculation would 
be comparatively easy ; but we prefer at present merely con- 
fining ourselves to simple illustrations of our theory. 

Thus, let us, for simplicity, assume that the magnetic matter 
of the earth is iron, with everywhere a coefficient of magneti- 
zation 

Ko): 
then the terms involving x’ will be large compared with the 
others ; so that if, for a very rough approximation, we assume 
a, to be nought, and a, equal to unity, or the whole earth to 
consist of iron, we find 
167 __cos@ 


=- ow =. 
ae ial 


Vv 


* «x for ordinary iron is probably between 20 and 30; and in our igno- 


rance of the internal state of the earth, or what effect the great heat or 
pressure may have on the coefficient of magnetization, we are compelled 
to use this value; but it is possible, of course, that the real value of x 
may be very different. 


Theory of Terrestrial Magnetism. 407 
Now Gauss gives for the magnetic moment of the earth, 
3°3092 n’, 


in millimetre-milligramme-second units, and where n is the 
number of centimetres in the earth’s radius. Consequently, 
since the dimensions of a magnetic moment are 


ML?T ’; 
the earth’s magnetic moment becomes 
00033092 n- 2 n', 


the units being the earth’s radius, gramme, second. 

Assuming Biot’s distribution of magnetic force over the 
surface of the earth, which is also what our theory has led us 
to, we then get from Gauss’s expression for the moment the 
result that the magnetic potential on the earth is 


0°33092 cos On—3, 
or 
0-00001311 cos @ nearly ; 
so that roughly we have, for a point on the earth’s surface, 


ws ow = 000001311. 


But yh Qer 
°= 94x 60 x 60 ? 
., the density 
o=0°0107 unit of electricity, 
or the total charge 
4a x HOLT, 


the fundamental units of space, mass, time being the radius of 
the earth, the gramme, and the second. But the dimensions 
of o are M? L*; so that, in order to express o in C.G.S. units, 
we must multiply by “n; therefore the total charge 


= 4m x 0°0107 /, ee UOE RON en Gigiet 
T 


= 4 x 0-01074/ ee x 10’ microfarads. 


To get an idea of the electromotive force required to pro- 
duce this charge, let us imagine one pole of a Daniell’s battery 
connected with the earth and the other with all bodies in space. 
Then, since the capacity of the earth is 630 microfarads, this 
charge will be produced for each cell so employed ; so that, if 


408 Professors Perry and Ayrton on a new 


«is the number of cells necessary to produce our required 


distribution, 
Ant x 0:0107 x 4 / 2% 10" 197 
T 
—- 630 
=54 million roughly. 


i —— 


We have therefore proved that if the earth be electrified, it 
must, from its very rotation, quite independently of all other 
bodies in the universe, be magnetic; and if it consist of a 
shell of iron, thick or thin, then that the law of distribution 
of magnetism produced by this electric charge in mechanical 
rotation will be identically that given by Biot; and, lasily, 
if the earth were wholly of iron, a difference of potentials of 
about fifty-four million volts between it and space would be 
sufficient to produce the necessary amount of charge. 

Now, although fifty-four million volts is a large difference 
of potentials to be produced with a galvanic battery, there 
would not be the slightest difficulty in the earth having such 
a difference of potentials between it and space, seeing that the 
earth is surrounded by millions of miles of interplanetary va- 
cuum, every inch of which is as good or better an insulator 
than a Crookes’s vacuum; and it has been experimentally 
shown that many thousands of cells will not cause a discharge 
across even a comparatively thin film of such a vacuum. 

But even without considering the highly insulating cha- 
racter of interplanetary space, we see from the experiments of 
Drs. De La Rue and Hugo Miiller that the electromotive force 
of fifty-four million cells cannot, in all probability, initiate a 
spark between two points in ordinary air unless the distance 
separating them be less than four hundred feet. Consequently, 
if the electric charge which by its mechanical rotation pro- 
duces the magnetism be on the earth itself and not in the air, 
it could not be discharged by sparking, unless another planet, 
having at least a potential nought relatively to the earth, came 
at least to within four hundred feet of its surface. 

Next, as regards the sign of the electric charge on the 
earth’s surface required to produce the earth’s magnetic pola- 
rity, is it in accordance with the known phenomena of atmo- 
spheric electricity? To produce the earth’s magnetism, we 
must have, in accordance with the known laws of electro- 
magnetism, a negative current flowing from west to east, or in 
in the direction of rotation of the earth. In the language of 
the new theory, therefore, the surface of the earth must be 
negatively charged ; but Sir William Thomson has proved, by 


3 3 
ee 


Theory of Terrestrial Magnetism. 409 


observations with his electrometer, that all the phenomena 
brought to light by atmospheric electricity, on a fine day, 
could be produced by the sole agency of the earth having 
a negative charge and without any charge in the air itself. 
The negative charge, therefore, required for our explanation - 
of the cause of terrestrial magnetism is sufficient to account 
for all the ordinary phenomena of atmospheric electricity. 

In the preceding investigation we have supposed the electric 
charge to be uniformly distributed over the earth, and so have 
arrived at a law of magnetic intensity merely varying with the 
latitude. But the sun and other members of the solar system 
may very likely have potentials so different from that of the 
earth that we can hardly conceive the amounts; consequently 
we should expect the static electric distribution of the earth 
would undergo periodic changes corresponding in time with 
those of the ocean-tides. But alteration in the static distribution 
of electricity on the earth’s surface means, as we have shown, 
alteration in the law of magnetic intensity ; consequently we 
should expect that this magnetic intensity would vary somewhat 
as do the ocean-tides ; and this is known to be the case. But it 
is also evident that, besides these regular changes, every time a 
great mass of vapour is suddenly formed and condensed on the 
earth, and whenever great changes are occurring in the solar 
atmosphere whereby the lines of electrostatic induction from the 
sun to the earth are altered, we should find corresponding 
changes in terrestrial magnetism such as we now know as 
magnetic storms. And not only this, but as the planets are 
charged bodies, their motions relatively to the sun ought to 
cause motions in the sun’s atmosphere such that, for instance, 
the allineation of a number of planets and the sun, or the near 
approach of any planets, if the alligned or approached planets 
have potentials nearer that of the sun than many of the other 
bodies of the solar system, ought to diminish the storms in the 
solar envelope, and ought to alter the electrostatic distribution 
on the earth. But it has béen shown that the near approach 
of a planet to the sun both affects the sun’s spots and terres- 
trial magnetism. 

And, lastly, since the iron in the earth may, from its great 
pressure, possess great coercive force, we should expect (as 
we know to be the case) that magnetic changes would lag 
behind the astronomical influences accompanying them. 


Addition, April 17th.—Since the reading of this paper be- 
fore the Physical Society, several criticisms have appeared of 
this proposed explanation of terrestrial magnetism. Some of 


410 On a new Theory of Terrestrial Magnetism. 


the writers have failed to realize that the various parts of a 
rotating sphere have relative motions one to the other, of such 
a nature that if some were electrified the others would become 
magnetized. Their difficulty seems to have arisen from the 
fact that the motion of a particle of a rotating rigid sphere 
consists of a rotation round the axis of the sphere com- 
bined with a rotation of the particle round its own axis; so 
that if two particles be looking at one another in one position 
of the sphere, they are looking at one another in all positions, 
just as the same side of the moon is always turned to the earth. 
But if this rotation of the particles round their own axes could 
be stopped, if, in fact, the motion of the particles became 
what is commonly known as “ sun-and-planet motion ”’ similar 
to that of the bobbins in the machinery used in sheathing tele- 
graph-cables to prevent torsional strain being put into the 
iron wires as they are lapped on the core), then probably these 
writers would have no difficulty in seeing that the interior 
particles would be magnetized by the more rapidly moving 
electrified ones. Now the motion of an wnelectrified particle 
round its own axis cannot in any way prevent it becoming 
magnetized by electrified particles revolving round it; for 
if it could, it would be equivalent to saying that, if the elec- 
trified particles were at rest and the wnelectrified one revolving, 
the mere revolution of the latter would magnetize itself 
oppositely to the way it would be magnetized if it were at rest 
and the electrified ones only in motion—a result not only 
without experimental proof, but one also highly improbable. 
Consequently, if the particle has the two motions together (as it 
has in a rigid revolving sphere), it will still become magnetized 
if the surface of the sphere is electrified. 

In fact, so little can the motion of a mass of iron prevent 
its becoming magnetized by a moving charge of electricity, 
that it has been suggested to us, within the last few days, by 
Mr. G. F. Fitzgerald, of Trinity College, Dublin, that pro- 
bably a mass of iron would become magnetized by a static 
charge of electricity if both had rapid absolute motion in space, 
even although in the same direction in parallel lines and with 
the same velocity—in fact, that relative motion is unnecessary. 
If this assumption (which has not yet been experimentally 
tested) be true, then not only will the mathematical analysis 
required in the investigation of the problem contained in this 
paper be much simplified, but, in addition the charge of elec- 
tricity on the earth’s surface necessary to produce, by its me- 
chanical rotation, the earth’s known magnetic moment will be 
considerably less even than the charge calculated above. We 
hope to put this idea of Mr. Fitzgerald’s shortly to an experi- 


Maintenance of Constant Pressures and T. emperatures. All 


mental test ; but in the meantime we give no further indica- 
tion of the reasoning by which it has been arrived at, nor of 
the way in which our equations would be modified, preferring 
to leave the investigation in a perfectly rigid form as it now 
stands, rather than to introduce any assumption which might 
appear problematical, even although such an introduction 
would both add weight to our theory, and might explain, from 
the velocity in space of a place at midnight being greater than 
at midday, the cause of the solar-diurnal magnetic variation. 


LXIV. The Maintenance of Constant Pressures and Tempe- 
ratures. By FREDERICK D. Brown, B.Sc.* 


[Plate XIII. ] 
bee great majority of the results obtained from physical 


experiments vary with the temperature at which the 
observations are made. The measurements of the density of a 
substance, for example, of its refractive index, of its electric 
conductivity, of its elasticity, of the maximum tension, and of ° 
the latent heat of its vapour, all require that the temperature 
should not vary during the observations. Hitherto many of 
these measurements have been confined to temperatures dif- 
fering little from that of the atmosphere; such temperatures 
are easily maintained constant by means of a bath of water or 
other liquid; but when we try to make observations at higher 
temperatures, the means at our disposal fail us, and we find 
that, except at certain points (such as 100°), we cannot keep 
up the same temperature long enough to make at leisure ac- 
curate readings of our instruments. 

Many attempts have been made to obviate this difficulty, 
but, as it seems to me, without complete success. The ordi- 
nary method has been to use a large quantity of water or 
other liquid, and to keep it in continual agitation; above 
50°, however, the temperature of such a bath is rarely, or 
never, rigorously constant, while the inconvenience and waste 
of time incurred in heating the large mass of liquid to the re- 
quired point are by no means to be neglected. 

In order to keep such a bath at a constant temperature, a 
large number of gas-regulators have been invented. In most 
of these a small vessel containing mercury or air is placed in 
the bath, and arrangements are made by which the gas-supply 
is partially shut off when the mercury expands beyond a cer- 
tain point. Probably the most sensitive form of this kind of 
apparatus is that recently described by M. Benoit to the French 


* Communicated by the Physical Society. 


412 Mr. F. D. Brown on the Maintenance of 


Physical Society. Here a small closed vessel containing methyl 
acetate is placed in the water the temperature of which is to 
be maintained constant; this vessel communicates with a ma- 
nometer containing mercury ; and as the vapour-tension of 
the methyl acetate increases, the mercury in the manometer 
rises, obstructing the flow of gas to the burner in the usual 
way. 7 
has applied this form of thermostat to a bath of water 
used for heating along column of mercury. The water is con- 
tained in a vertical copper cylinder 42 inches in length by 6 
in diameter; the cylinder is packed with felt on the outside, 
and contains within it a second smaller and shorter one open 
at both ends, and extending to within about 2 inches of the top 
and bottom. By means of a suitable mechanical arrangement, 
the water is made to flow continuously down the space be- 
tween the two cylinders and up the inner cylinder; the upper 
and lower portions of the bath are thus kept at exactly the 
same temperature. The water is heated by allowing it to cir- 
culate through a copper coil placed over a gas-burner. Hven 
when the small vessel of the thermostat is filled with ether, 
_ the tension of which varies much more for a given variation of 
temperature than does that of methyl acetate, the temperature 
is subject to fluctuations of as much as 0°1, and this indepen- 
dently of the change which necessarily occurs when the pres- 
sure of the gas is altered. . 
Gas-regulators are employed perhaps more successfully 
where the gas-flame can be applied directly underneath the 
bath ; for the rise of temperature in the water then follows 
more rapidly upon the increase of the flame, the flow of gas 
is sooner checked by the mercury, and the tendency to allow 
too much heat to be communicated to the water is thereby 
lessened. Still better results are obtained if the thermostat 
be applied to an outer jacket of water surrounding the bath in 
which the observations aremade. Both these conditions, how- 
ever, are generally very difficult to carry out where large 
quantities of water are of necessity used. Hven when all 
these precautions are taken, a constant temperature, in the true 
meaning of the words, is not attained. For a further discus- 
sion of the defects of this form of thermostat see Laspeyres*. 
The only practicable way of attaining the object in view ap- 
pears to be afforded by the fact that the vapour emitted by a 
boiling liquid does not vary in temperature, provided that 
there is no variation either in the composition of the liquid 
or in the pressure to which it is subjected. Taking their 
stand on this consideration, Laspeyres (loc. cit.) and Sprengel 
* Pogg. Ann. clii. p. 132. 


Constant Pressures and Temperatures. 413 
(Journ. Chem. Soc. 1873, p. 458) suggested the use of mix- 


tures of sulphuric acid and water of different strengths, which, 
if the vapour given offis condensed and returned to the mass, 
boil constantly at certain given temperatures: here the constant 
temperature is afforded by the liquid and not by the vapour, 
which is less hot; hence, if the liquid tends to become super- 
heated, fluctuations in temperature will infallibly occur. The 
great objection to this method is that, when a series of tempe- 
ratures is required (as, for instance, in the comparison of ther- 
mometers), great inconvenience and loss of time is incurred by 
having frequently to replace the liquid in the apparatus by 
another containing a different proportion of sulphuric acid or 
other substance. 

A series of temperatures can be obtained with one liquid 
only, if the pressure under which it boils be varied. ‘This 
method, simple as it appears, is beset with considerable me- 
chanical difficulties, to surmount which the apparatus described 
below has been constructed. 

At first sight it would seem that, if the vessel containing the 
steam be connected with a large closed vessel serving as air- 
reservoir, all that is necessary is to rarefy or compress the air in 
the reservoir to the required extent, and to allow the liquid to 
boil undisturbed. But the steam-bath is necessarily large; and 
the reservoir therefore must be large also. Now the reservoir 
must not only be strong enough to stand a vacuum inside it, but 
must also be capable of supporting an interior pressure of at 
least 50 Ibs. on the square inch; such a reservoir is not only 
cumbrous and expensive, but dangerous. Further, any change 
of temperature in the room alters the pressure inside this reser- 
voir ; it must therefore be placed in a cistern of water, which is 
a second objection. The great obstacle to the employment of 
this method, however, is the difficulty of preventing leakage 
even with the greatest possible care. In endeavouring to stop 
leaks ] expended so much time that I gave up the reservoir, 
and determined to construct an apparatus for maintaining a 
constant pressure in a given vessel even when it leaked. 

Lothar Meyer (Ann. Chem. Pharm. vol. clxv. p. 808) had 
already devised an apparatus of this kind, adapted chiefly to 
fractional distillation under reduced pressure. It consists essen- 
tially of two vertical tubes, A Band C D(fig.1, Pl. XIII.), con- 
nected at the upper part by the lateral tubes H and F; at B an 
india-rubber tube connects A B with the tube K, which slides 
up and down the board to which the whole is fixed ; at the top 
of A Bisa tube H which is connected with an air-pump ; the top 
of C D is provided with a cork, through which a narrow tube SS 
passes nearly to the bottom of C D; finally, the lateral tube & is 


Phil; Mag. 8. 5. Vol. 7. No. 45. June 1879. 2] 


414 Mr. F. D. Brown on the Maintenance of 


connected with the apparatus X, in which a constant pressure is 
kept up. Sufficient mercury is poured into R to fill A B up to 
the lower end of H when Ris about half full; C D is also filled 
with mercury, which is let out by the tap M until the column 
P § above the lower end of SS is equal to the difference be- 
tween the required pressure and that of the atmosphere. If 
now the air-pump be set to work, a partial vacuum will be 
created in X and in the tubes A B and C D, the mercury will 
rise in A B until it touches the lower end of H; Ris then placed 
in such a position that the vertical distance between the lower 
end of H and the surface of the mercury in R is equal to PS. 
It is now evident that when the desired pressure is reached 
the mercury will close up the orifice of H, thus stopping the 
withdrawal of air; while if the pressure is less than that re- 
quired, more air will enter through the tube 8S and bubble up 
through the mercury, and thus a more or less constant pressure 
will be maintained in X. . 

This apparatus suffers from two defects: first, the splash- 
ing of the mercury as it is sucked up H and then falls down 
again, together with the bubbling of air up C D, renders the 
pressure in X slightly variable; secondly, it is only adapted 
_ for pressures less than that of the atmosphere. 

_ Meyer’s instrument has very recently been modified by Dr. 

Otto Schumann and by W. Stadel and E. Hahn (Ann. Chem. 
Pharm. vol. exev. p. 218); the new form, although capable 
of regulating pressures above an atmosphere, apparently with 
tolerable accuracy, has a very limited range. 

The apparatus for maintaining constant pressures, which I 
now wish to bring to the notice of the Society, consists of a ma- 
nometer connected with which is an automatic arrangement for 
governing the supply of air. The manometer (fig. 2) consists of 
a tube A B having the form and dimensions shown in the figure; 
the lateral tube C is connected with the vessel X, in which a 
constant pressure is to be kept up; the tube D is connected 
with an air-pump or other contrivance for rarefying and com- 
pressing air. The upper end of the tube A B is closed by an 
india-rubber stopper, or, better, by a metal cap, through which 
the rod H, passes air-tight; this rod is tipped with platinum 
at its lower end. The lowerend of A B is joined by means of 
india-rubber tube to the tube I’, of which the upper part has 
the same diameter as that of AB; this tube is fitted with 
another cap and iron rod EH, similar to the first ; but the cap 
does not fit air-tight. The piece of wood which carries F 
moves along the scale SS in a groove in the board to which 
the whole is fixed. Lastly, the two rods E,, E, are furnished 
with binding-screws for copper wire, while a third binding- 


Constant Pressures and Temperatures. 415 


screw K is connected with a small piece of steel tube inter- 
posed between the end of AB and the india-rubber tube. 
This third connexion with the mercury contained in the mano- 
meter may of course be made by means of a third (insulated) 
rod passing down to the bottom of the wider part of A B or F. 

To fill and adjust the manometer, the tube F is raised to the 
same level as A, and mercury is poured in until it just reaches 
the wide cylindrical portions of A and F’; the rods E,, E, are 
then moved until the point of H, just touches the surface of 
the mercury, while that of EH, is a fraction of a millimetre 
above it. : 

Suppose now that I’ be lowered n millims. and the air- 
pump be set to work to pump air out at D; further, that K 
be connected with one pole P of a battery, and the rods 
Hi,, E, with the other pole N; then it is evident that as long 
as the pressure in A, and consequently in X, is greater than 
H—n (where H= the barometric pressure), the current will. 
pass through the circuit P K H, N, whereas when the pressure 
is less than H—n the current will pass along PKE,N. 
Similarly, if F be raised n millims. above A and the pump be 
made to compress air into A, as long as the pressure is less 
than H-+7n, the current will pass along P K H, N; but when 
the pressure becomes greater than H +7, the current will pass 
along PK E,N. In order to economize space, the tube A B 
is widened out at B; and when it is intended to obtain a 
pressure greater than H, the rod H, is replaced by a long one 
reaching down to B; this, of course, is equivalent to lowering 
A or raising F' nearly the whole length of the scale SS. In 
the further description I shall only consider the case in which 
F is lower than A—that is, when a pressure less than H is 
required; the alteration needed for higher pressures will readily 
suggest itself. 

_The apparatus depicted in fig. 3 consists of a brass tap T and 
an electromagnetic clutch to work the tap automatically. The 
tap, which is shown in section in fig. 4, is placed between the 
tube D of the manometer (fig. 2) and the air-pump, L, being 
connected with D and L, with the pump. From the figure it 
is readily seen that when the tap is in the position drawn, and 
the lever fitted to the head of the key lies in the direction a6, 
air will be admitted into the manometer ; if, on the other hand, 
the lever and key occupy the position a’ b’, the pump will with- 
draw air from the manometer. The object of the clutch, there- 
fore, is to place the tap in the first position when the pressure is 
too small, and in the second when itis too great. The lever ab 
(fig. 3) terminates in two ares which are grooved to hold a cord; 
these arcs are furnished with set screws §,, 82, by means of which 

iA 


416 Mr. F. D. Brown on the Maintenance of 


the amount which the tap can open may be regulated. The 
two ends of the lever are connected by strings at §; 8, to the 
loose pulleys P, P, of the clutch. These pulleys are made of 
soft iron, and run on a spindle which revolves on the centres 
A, A;. Revolving with the spindle and facing P, and P, are 
two small electromagnets M,, M,: one end of the coils of each of 
these magnets is soldered to the insulated ring I,; the two other 
ends are soldered to J, and I; respectively. The binding-screws 
U,, U2, U; are connected electrically by means of springs with 
these rings; U, is further connected with the pole N of the 
battery, while from U, and U; wires run to EH, and Hy respec- 
tively. The disposition of the wires is shown in fig. 5: it is 
there evident that if the mercury in the manometer touches 
the rod H,, M, will become magnetic; the loose pulley P, 
(fig. 3) will then tend to revolve with it, and the tap will take 
up the required position ab; while if the mercury touches Hg, 
M, will become magnetic, P3; will revolve, and the tap will 
assume the position a’b’, in which communication is made 
with the air-pump. By this arrangement, therefore, the pres- 
sure in the manometer, and in whatever apparatus is connected 
with it, is caused to rise and fall within very small limits; with 
care these limits may be made to differ only about 0°25 millim. ; 
and thus a practically constant pressure is attained. 

The current required to work the magnets is no more than 
is furnished by a small Smee’s cell; the magnets may be 
made to revolve with a small turbine; the air-pump may be 
replaced by a Bunsen water-pump; an air-pump, however, 
is the only convenient apparatus for compressing air. 

It may be objected that the arrangement above described 
requires motive power, which is not always at hand in a labo- 
ratory. To meet this objection I endeavoured to construct a 
double valve to be moved to and fro by two stationary mag- 
nets; but I found that magnets of ordinary size were not 
powerful enough for the work, as the valve, to be of any use, 
must fit perfectly air-tight, even when subjected to very high 
pressures. I have not, however, given much attention to this 
point, an engine which I use for many other purposes being 
obviously the best source of the necessary power. 

In fig. 6 is given a section of the steam- or vapour-bath which 
I employ for the comparison of thermometers and for the 
measurement of the expansion of liquids in dilatometers ; it is 
also suitable for the direct comparison of thermometers with a 
standard air-thermometer. The bath is made of brass, and 
consists merely of a boiler B surmounted by a double tube 
D ,D similar to those first used by Rudberg and Regnault for 


Constant Pressures and Temperatures. A17 


the upper fixed point of thermometers; the vapour, after tra- 
versing this, passes into the U-shaped condenser OC, from 
which the condensed liquid runs back into B down the tube 
Hi. The end H of this condenser is connected with the lateral 
tube C of the manometer by means of a very small lead pipe; 
and thus the liquid can be made to boil under any required 
pressure. The thermometers or other instruments are placed 
in the’small tubes TT, which are filled with petroleum of high 
boiling-point. Besides water, the best liquids for generating 
the vapour appear to be carbon disulphide for low, and purified 
paraffin oil for high temperatures; the latter substance I have 
not hitherto used, as I have had no occasion to make observa- 
tions at such temperatures. I have, however, made experi- 
ments with it in a smaller apparatus of similar form, and found 
that no variation of temperature took place. 

The temperature obtained from these three liquids may be 
varied from 25° to 300° without unduly increasing the 
pressure. 

If the temperature in the double tube D D be observed with 
a thermometer of which each degree is 5 millims. long, no 
variation can be detected, even with an extremely rigid cathe- 
tometer, provided, of course, that the barometric pressure does 
not alter; the variation due to this cause might, if necessary, 
be removed by making the cap of the tube F of the mano- 
meter fit air-tight. When great accuracy is necessary, it is 
not advisable to decrease the pressure below 100 millims. 

In order to see whether the whole length of D D is at the 
same temperature, small oblique tubes similar to T were in- 
serted, one at the top, the other at the bottom; a thermometer 
placed first in one and then in the other of these, gave exactly 
the same reading in both. 

To sum up. First, with the above apparatus, viz. a mano- 
meter communicating by means of a specially constructed tap 
worked by a double electromagnetic clutch with a constantly 
working air-pump, any given pressure may be maintained for 
an indefinite period without varying more than 0°25 millim.; 
secondly, if this constant pressure be applied to a suitable 
vapour-bath, any given temperature between 25° and 300° 
may be maintained absolutely constant as long as no chemical 
change occurs in the liquid whence the vapour is derived. 


[ 418 ] 


LXV. Considerations on the two Memoirs of Sir B. C. Brodie 
on the Calculus of Chemical Operations. By M. A. Naquet*. 


ii is not our intention here to express a complete judgment 

upon the work of Sir B. C. Brodie. This work comprises 
a mathematical part, of which we are not competent to judge, 
and a chemical part, upon which we have the right of pro- 
nouncing. It is with the latter alone that we mean to occupy 
ourselves here. | 

We may begin by saying that whatever may be the final. 
judgment pronounced upon the work of Sir B. C. Brodie, that _ 
work appears to us remarkable ; and it is that which has in- 
duced us to make it known to the French public. 

The application of Algebra to the experimental sciences, the 
substitution of “ theories,’ based upon facts and demonstrated 
laws, for ‘ systems ’’ which only rest upon metaphysical hypo- 
theses, is the end towards which science ought to tend; andif 
systems are necessary for the arrangement of phenomena, and 
for the discovery of new phenomena in those points where the 
progress of science has not yet allowed them to be replaced 
by theories, this substitution ought, nevertheless, to be effected 
as soon as practicable. ? 3 

We will say at once that Sir B. Brodie is unjust in denying 
the discoveries which are due to the atomic notation. It is 
by means of this notation and the probabilities deduced by it 
that a number of syntheses have been effected—such, for ex- 
ample, as the synthesis of the phenols, those of the acids of the 
salicylic series, of secondary and tertiary ammonia compounds, 
etc. etc. How could it, in fact, be otherwise? As M. Dumas 
says, in his ‘ Lecons de philosophie chimique,’ a hypothesis 
created for the explanation of twenty phenomena, to which it is 
adequate, is necessarily applicable to ten, twenty, thirty other 
unknown phenomena on the track of which it places the ob- 
server. But, while fully recognizing the superiority of a 
“theory ’’ over a system, we refuse to abandon our system 
unless the theory be complete enough to render all the services 
which the system has rendered. It does not. appear to us that 
at present the notation of Sir B. Brodie has gone so far as to 
be able completely to replace the existing notation; but I do 
not consider these reasons sufficient to condemn it. 

When Gerhardt modified the notation in use before his 


* M. A. Naquet has translated into French the two memoirs referred 
to, on which translations the critical observations of M. A. Naquet are 
based. These have been translated into English under my supervision.— 
B. C. B. (Moniteur Scientifique du Docteur Quesneville, Noy. 1878, 
March and April 1879.) 


On the Calculus of Chemical Operations. 419 


time, this notation did not assume at first the form it has since 
acquired : it has been perfected, modified, almost transformed ; 
it is, however, from Gerhardt that it dates, and to him the 
honour of it is due. Similarly Sir B. C. Brodie makes a bold 
attempt on a new path which may lead to great results; and 
we must beware of rejecting what he brings on the ground 
that it is incomplete. The mathematical analysis proposed by 
him is as yet but a germ; worked out and developed, it may 
become an organism. ; 7 

This said, and all reservations made as much in favour of 
as against the new method, we may say at once that the ex- 
isting atomic notation may be divided into two parts :—that 
which is entirely hypothetical and metaphysical, and which 
explains phenomena by the grouping of atoms ; and that which, 
in spite of the words atom and molecule which offend Sir B. C. 
Brodie, is not more hypothetical than the notation of Sir 
B. C. Brodie himself. The whole is, in fact, a matter of de- 
finition. How do we define a molecule? It is the smallest 
portion of matter at which we can arrive by physical division, 
and of which the weight is equal to two volumes of the vapour 
considered in relation to the weight of one volume of hydrogen, 
both at the normal conditions of temperature and pressure. 
How do we define an atom? It is the smallest quantity of a 
given portion of matter attainable by chemical division, which 
is not subdivided in any operation, and which is always trans- 
ported integrally from one combination to another. A mole- 
cule, then, setting aside all metaphysical senses, is the weight 
of two volumes of a gas or a vapour ; an atom is the weight 

-of two, of one, or of half a volume of a gas or a vapour, ac- 
cording as, in chemical reactions, the molecule is transported 
intact or is subdivided into smaller weights. 

Now what does a “ simple weight ”’ represent for Sir B.C. 
Brodie? It is a weight which in being transported from one 
combination to another is not “distributed.’”” What does a 
compound weight represent to him? It is a weight which in 
the course of chemical operations is divided, is “ distributed.” 
Finally, what does he term the “unit of ponderable matter ”’? 

_ The weight of one volume, say of 1000 cub. centims., of a gas 
or of a given vapour. 

Let us suppose that Sir B. C. Brodie had accepted his hy- 
pothesis «’ instead of stopping at the hypothesis a. ~All his 
units would then become equal to our molecules ; those of his 
“units? which were not “distributed ’’ would have been 
identical with those of our molecules (mercury, for instance) 
which we consider as composed of a single atom. Those of 
his “ units’’ which were “distributed’’ would have been 


420  M. A. Naquet on the Calculus 


identical with those of our molecules which we consider as 
composed of several atoms. It is, in fact, absolutely identical 
to take H=1 and to bring all the molecules to two volumes, or 
to bring all the molecules to one volume and to take H=4. 
The numbers obtained would be the same in the two cases. 

Now, if Sir B. C. Brodie has been induced, by the serious 
considerations given in his memoir, to prefer the hypothesis 
a to the hypothesis «’, he does not, however, consider the hy- 
pothesis a? as more metaphysical, less scientific than the other ; 
and if it had not been his object to explain the “ law of even 
numbers,” he would have adopted it*. 

With the hypothesis «’, there would have been nothing 
different between our notation and that of Sir B. C. Brodie, 
nothing except the substitution of the words “ units,” “ dis- 
tributed weights,” “ simple weights,” for the words “ mole- 
cules,’ ‘molecules composed of several atoms,’ and 
“atoms.” Now, when it is well understood that no impor- 
tance, no metaphysical signification, is attached to the 
words “ molecules’? and atoms,” but that the expressions 
are simply taken as indicative of facts previously announced, 
the question of words signifies nothing, and it matters little 
whether the same ideas are expressed by “ molecules” and 
“atoms,” or by “ units,’ “simple or undistributed weights,” 
and “compound or distributed weights” t. It matters no 
more than it matters whether a given thought be expressed in 
one language or in another, provided that the expression be 
clear and unequivocal. 

Let us go farther. Sir B. C. Brodie recognizes that certain 
“ weights’ which are regarded absolutely (that is, when the 
whole of the chemical system is considered) as ‘ compound or 
distributed,’ cannot in a limited system of operations be dis- 
tributed, and act like “simple weights.” These are “simple 
relative weights.’? Now, when we give the name of “ com- 


* The fact is that; but for the law of even numbers, the system « could 
not be constructed at all.—B. C. B. 

+ All this is perfectly true ; but it is eminently undesirable to express 
different ideas by the same term, which leads to confusion. The ideas ex- 
pressed by the terms ‘simple weights” and “ undistributed weights,” 
are not the ideas expressed by the terms “atoms” and “ molecules,” but 
rather those ideas divested of what M. Naquet terms their ‘ metaphysical 
signification,” which are not the same thing. Indeed the advocates of 
the atomic basis of Chemistry would not, I imagine, be very well pleased 
with M. Naquet’s description of an atom as “a metaphysical entity.” 

The identity of system «? with our present system is limited to the 
identity of the notation by which the units of matter are expressed. The 
Algebraical method of working with these symbols as developed in Part IL., 
which is an essential feature of this Calculus and peculiar to it, is not 
found in our present system.—B. C. B. 


of Chemical Operations. — 421 


pound radical” to the portion of matter represented by C,H, 
or C,H;, for instance, we do not express any other idea. The 
compound radical represents to us a portion of matter which 
in the series of phenomena under consideration is transported 
integrally from one combination into another, although it may, 
in other circumstances, be decomposed into simpler elements. 
“ Compound radical,” or “simple relative weight,” are there- 
fore one and the same thing. Here, again, is a matter of 
- words. 

We may add that the substitution of hype thesis a for hypothe- 
sis a” isnot fundamental. If, supposing that Sir B.C. Brodie had 
not written his two memoirs, it had been shown that the bodies, 
so called, of uneven atomicity contain hydrogen, and correspond 
to the general formula HR, or H,Ry,, immediately our existing 
notation would be transformed, except for the use of Greek 
letters, into that of Sir B. C. Brodie, without any alteration 
in the general system, unless it were the important discovery 
of the compound nature of a series of bodies hitherto con- 
sidered as elementary. d 

To set against this‘there is in the existing notation a series 
of hypothetical considerations for the expression of fine iso- 
mers, which Sir B. C. Brodie rejects. Thus, when we ex- 
press the isomeric relations of aldehyde, acetylenic alcohol, 
and oxide of ethylene by the formule 


C== pk. Crax rks Gans Els 
|——4 . H (=H 
eee OQ” OT Ot =} 2 


we make a hypothesis on the mode of grouping these atoms 
considered as metaphysical entities. 

It is the same when we try to account for the differences 
existing between isomers such as salicylic, oxybenzoic, and 
paraoxybenzoic acids, and explain them by the place occu- 
pied in relation to each other by the groups OH and CO,H 
and the benzol-group C, Hg. 

We will return presently to this hypothetical part of our 
notation. Let us pause for a moment on the part common to 
the existing notation and the notation of Sir B. C. Brodie, and 
see if, in fact, the hypothesis a, setting aside the difficulty 
caused by the necessity of considering as compounds a mass 
of simple weights, offers the advantages over the hypothesis «” 
which Sir B. C. Brodie asserts. According to him, a hypo- 
thesis is acceptable when it accounts for all the known facts. 
Of two hypotheses which equally account for all the facts, that 


422 M. A. Naquet on the Calculus 


one ought to be preferred which is the more limitative. In 
other words, if a hypothesis A accounts for all the facts and 
does not suggest any improbable phenomenon, while another 
hypothesis A, accounting equally for all the known facts 
suggests a considerable number of unknown and improbable 
facts, it is hypothesis A which we ought to select. 

We fully accept these principles; but let us see their con- 
clusions. The hypothesis «, Sir B. C. Brodie says, permits 
the regular explanation, by means of integral positive factors, - 
of the symbols of all the known facts. But it admits besides 
of the similar construction of symbols of an equal number of 
substances which the law of even numbers rejects as impossible 
to realize. The hypothesis a, on the contrary, while per- 
mitting the expression by symbols, by means of integral posi- 
tive factors, of known facts, excludes the possibility of repre- 
senting in the same way, by means of symbolic expressions, 
the substances which do not obey the law of even numbers. 
The hypothesis « is therefore superior to the hypothesis a”. 

Such is the argument of Sir B. C. Brodie; and we should 
consider it irreproachable if hypothesis: « were not, though 
more limitative on one side, more extensive on the other, and 
if, from this point of view, what is gained in one sense were 
not lost in an opposite sense. 

But, first, the hypothesis « compels us to admit that chlo- 
rine, bromine, iodine, nitrogen, phosphorus, arsenic, antimony, 
bismuth, potassium, sodium,.etc., are compound bodies cor- 
responding to the general formula HR, or H,R,. This is a 
serious obstacle against accepting this hypothesis; for though 
there may be nothing impossible in this supposition, neither is 
there anything demonstrated : we anticipate experience, and 
thus we enter upon a path which threatens to lead us far. 

This is not all. The existing theory, which considers chlo- 
rine, bromine, iodine, nitrogen, etc. as elementary bodies, leads 
us to consider as products of “ substitution ”’ the compounds 
resulting from the action of chlorine, bromine, or iodine on 
organic hydrogenized bodies, as wellas the compound ammo- 
nias produced by the action of simple ethers on ammonia. 
The number of these products is thus limited. 

Let us take, for example, the action of chlorine on marsh- 
gas, CH,. Theory. indicates that this action ought to pro- 
duce four bodies, and four bodies only, as indicated in the 
the following equations :— 

7 CH, +Cl,=HCl+CH; Cl, 
CH, Cl + Cl,=HC1+ CH, Cl,, 
CH, Cl,+Cl,=HCl+CH Cl, 
CH Cl;+Cl,=HCl+ CCl, 


of Chemical Operations. — 423 


And, in fact, the action of chlorine on marsh-gas produces 
four products of substitution—chloride of methyl CH; Cl; 
chloruretted chloride of methyl, CH, Cl,; chloroform, CH Cl;; 
perchloride of carbon, C Cl,—and four only. 

Similarly, ammonia having as its formula NH3;, and chlo- 
ride of ammonium NH, Cl, we ought to be able to substitute 
three alcoholic radicals for the hydrogen of ammonia, and four 
of these radicals for the hydrogen of ammonium contained in 
the ammonia chloride, whence result three compound free 
ammonias and three only, four compound ammoniums in the 
state of combination and four only, as indicated by the fol- 
lowing equations :— 


NH;+C, H; [= HI+NH,(C, H;) =ethylamine ; 
NH,(C, H;) +0, H; l= HI+ NH (C, H;).=diethylamine ; 
NH (C, H;),+C,H;I=HI+ N (C, H;)3;=triethylamine ; 

N(C, H;)3+C, H; l=N(C, H;), 1=iodide of triethylammo- 
nium. 


And this is, in fact, what occurs: each compound monatomic 
alcohol-radical produces three compound free ammonias and 
one quaternary ammonium, and these four ammonia derivatives 
only. Finally, from the relations which exist between the de- 
rivatives of the chlorine substitution of hydrocarbons and 
alcohols, the latter also are considered as products of sub- 
stitution resulting from the exchange of H, Cl, Br, or I for 
the group OH. From the relations which connect alcohols 
to aldehydes, aldehydes to acids, acids to amides, the number 
of alcohols, acids, aldehydes, and amides is limited, like that of - 
the chlorine derivatives, by the number of chlorine derivatives 
contained in each hydrocarbon. 

It is not the same with Sir B. C. Brodie’s notation. Marsh- 
gas, for example, being «” «(=CH,, C=6), and chlorine being 
ay”, the reaction of chlorine on the hydrocarbon becomes 
ate. + ay” = ay -- KY. 
ee kee ——— SS 

Marsh-gas. Chlorine. Chlorhydrie Chloride 
acid. of methyl. 
That is to say, the chloride of methyl, which in our notation 
corresponds to the formula CH; Cl, and represents a product 
of substitution of chlorine for hydrogen, in Sir B.C. Brodie’s 
notation represents a simple addition of the prime factors 
of chlorine y» to marsh-gas. Similarly, methylic alcohol, 
CH;, OH, which in our notation is a product of substitution, 
becomes in the new notation «*«€—that is to say, a simple 
product of addition. 


424 M. A. Naquet on the Calculus 


It is the same for the compound ammonias. The equations 
by which we have represented the formation of these bodies 
take, in Sir B. C. Brodie’s notation, the following form:— — 


ano + ay = aw + atKy. 
Se eS ad SS — 
Iodide of Ammonia. lJIodhydric Ethylamine. 
ethyl. acid. 
aka + atk’y = awta’xty = diethylamine, 
ako + akkty = awt+a®%*’y = triethylamine, 
ae’o + ak’y = an®wv = iodideof triethylammonium. 


That is to say, the ammonias and the compound ethylic salts 
of ammonium result simply from the addition of ethylene, 
ax’? to ammonia, or to the salts of ammonium. We have, 
in fact, 


ay + ak? = a*x’y =ethylamine; 
on — 

Ammonia. Ethylene. 
ak’y + ak? = & x*y =diethylamine; 
a eee) 

Ethylamine. Ethylene. 

bkty + ak? = oo ey =triethylamine ; 
ss 

Diethyl- 

amine. 
cov + (ax’)* = a x*wv=iodideof tetrethylammonium. 
Sa 

Iodide of 

ammonium. 


Now, since Sir B. C. Brodie rejects every atomic speculation 
which would necessarily place a limit to these different addi- 
tions, his theory shows for each hydrocarbon an indefinite 
number of chlorine, bromine, or iodine derivatives, and an 
equally indefinite number of alcohols, aldehydes, and acids; it 
shows also an indefinite number of compound ammonias for 
each alcohol, of amides for each acid, &c. &e. 

We can, in fact, according to the new system of notation, 
perform upon the symbol of perchloride of carbon, «’x,*, the 
same operation that we can perform upon marsh-gas, perchlo- 
ride of methyl, chloruretted chloride of methyl, and chloro- 
form themselves. Thence we obtain the following equations:— 


ay + ay? = ay + aK’, 
Sa SS ve Sse 
Chloroform. Chlorine. Chlorhydric Perchtioride 
acids. of carbon. 
arKyt + ay? = ay + any? 
— 


SS Sy 
Perchloride Chlorine. Chlorhydric 
of carbon. acid. 


of Chemical Operations. 425 


It is absolutely impossible to express this last compound in 
our existing notation. 

Similarly, tetratomic alcohol, which would have for its for- 
mula C(OH),, an alcohol which is unknown, but of which the 
derivatives are known, ought to be written, according to Sir 
B. C. Brodie, #«§*. But Sir B. C. Brodie’s theory shows 
equally an alcohol 2’«é’, which our existing notation rejects as 
impossible. 

Finally, besides the triethylamine, («’«”)*)«’v, and the iodide 
of tetrethyl-ammonium («7x’)* (@’v) (aw), the notation of Sir 
B. C. Brodie shows the compound ammonias (@x?)"«’v and 
the compound iodides of ammonium, (a’«”)"+!(@’v) (aw). 
These last bodies, unlike the preceding, might be written in 
our existing notation, which would permit the expression of 
these compounds by the formulee 


(C, H,)"NH; and (C, H,)*+'NA, Cl; 


but our notation allows us also to consider them as compounds 
of substitution, instead of considering them as compounds of 
addition, which limits their number. 

Now, up to the present time there has never been obtained 
a number of chlorine, bromine, or iodine derivatives of a 
hydrocarbon greater than the number of the atoms of hydro- 
gen which this hydrocarbon contains. ‘There has never been 
obtained a number of alcohols greater than that of the chlo- 
rine, bromine, or iodine derivatives. Finally, there has never 
been obtained for each monatomic alcohol a number of com- 
pound ammonias greater than three, and a number of com- 
pound salts of ammonium greater than four. 

On the other hand, the law of even numbers, which Sir B. 
C. Brodie has so much at heart, is far from being demon- 
strated, since the exception of the oxides of nitrogen cannot be 
eliminated unless we admit the dissociation of our element 
nitrogen. But even if the law of even numbers were abso- 
lutely demonstrated, it would still not prove that a body which ~ 
cannot exist in a free state may not exist in a state of combi- 
nation. And, finally, if this explanation itself be inadmissible, 
since the notation a of Sir B. C. Brodie shows an innumer- 
able multitude of improbable bodies, and he does not point 
out to us any rule for eliminating them, which is contrary to 
that which actually occurs in the existing notation (and to 
that which occurs in the notation of Sir B. C. Brodie), for the 
bodies which do not satisfy the law of even numbers, the 
hypothesis « appears to us in all points inferior in the existing 
state of science to the hypothesis a”. 

Now the hypothesis a’ is nothing else than our existing 


426 M. A. Naquet on the Calculus 


notation without the speculations explanatory of the fine iso- 
mers mentioned above. Are these speculations, which could 
be perfectly well rejected even with our existing notation, 
out of date and already useless? Ido not think so. They 
may become useless one day. We shall perhaps find in ther- 
mochemistry the means of explaining these /ine isomers, and 
applying to them mathematical expressions. But until then 
these speculations appear to us useful, because they arrange 
facts which would otherwise remain without arrangement ; 
and they correspond well enough to the actual phenomena to 
allow us to determine, notably in the aromatic series, the 
number of these fine isomers possible for each term of the 
series. 

Hiven if we do not take into consideration the extreme dif- 
ficulty that there is in replacing one notation by another, and 
the momentary confusion introduced by it into science, a con- 
fusion which ought not to be permitted unless the change 
offers an undeniable advantage, even if we do not take into 
consideration this difficulty, we should oppose the immediate 
adoption of Sir B. C. Brodie’s notation, because it seems to 
us to open the door to a crowd of suppositions more consider- 
able than those it aims at eliminating, and because, from the 
point of view of the arrangement and anticipation of facts, it 
does not provide us with the means of dispensing with those 
atomic speculations which, without being intimately connected 
with the existing notation, may nevertheless be joined to it, 
and cannot in any case be adapted to the notation of Sir B. 
C. Brodie. 

Are we then to conclude that Sir B. C. Brodie’s work has 
no value? Far from us indeed be such a thought. If we had 
been of this opinion, we should not have taken the trouble to 
translate it. It opens out a new method which, enlarged and 
perfected, will permit the application of Algebra to Chemistry, 
and the substitution for our “system of chemistry” of a true 
‘theory of chemical events.”’ Hven if this result be not pro- 
duced, if the imperfections with which we charge the new me- 
thod of notation continue to exist, if there only remain of the 
notation of Sir B. C. Brodie his hypothesis «, including that 
of the compound constitution of chlorine, nitrogen, potas- 
sium, and their compounds, the work would still be useful. 

As long as we have to do with a “system,” a hypothesis 
with no other object than that of arranging known facts and 
discovering new facts, two ditterent hypotheses may legiti- 
mately be employed, provided that they answer to the requi- 
site conditions. It is thus. that the hypotheses of emission 
and undulations have long been tacitly accepted in Optics. It 


of Chemical Operations. 427 


might happen in this case also that two different hypotheses, 
both including the whole of the known phenomena, should 
lead to different deductions, and present different consequences 
which should guide the operator into two distinct paths. 
When things occur thus, it is useful to accept the two hypo- 
theses at once, and since no objective reality is attributed 
to them until experience has decided (when experience can 
decide), both are undeniably useful. Sir B. C. Brodie’s 
system, by showing the possible decomposition of the whole of 
one class of our elements, and by indicating one of the pro- 
bable cases in which these elements are decomposed (the cases 
of binoxide and tetroxide of nitrogen), renders a real rervice- 
to chemical science, and deserves to be known and studied. 
Ii will deserve this still more, if it be found that in working it 
out and perfecting it its defective sides are caused to disappear 
and its completion effected. It will help to place Chemistry 
on a solid foundation; and such an attempt has a right to the 
sympathetic attention of the whole scientific world. 


Postscriptum. Since these lines were written some curious 
observations have allowed scientific men to consider as pos- 
sible, as even probable, the production of free hydrogen by 
the action of an extremely elevated temperature on the greater 
number of our elementary bodies. Itis useless to demonstrate 
—it demonstrates itself—the value which this discovery, if it 
is confirmed, would give to Sir B. C. Brodie’s hypothesis. 


Note on an Objection made by M. Naquet in his preceding 
“Observations.” By Sir B. C. Broviz, /.R.S.* 


M. Naquet has had the kindness to forward to me the proofs 
of his “ Considerations”’ on my Memoirs. It is not my wish 
to comment here on his remarks; but there is one point in 
reference to which the remarks of M. Naquet are founded on 
a pure misapprehension of the state of the case. This point 
is of fundamental importance; and I will give a few words of 
explanation in regard to it. Indeed, if the difficulties which 
he has created really existed, the atomic method would have 
in some respects a great advantage over the method of this 
Calculus. I will explain the matter as briefly as possible. 
The objection of M. Naquet is this. We may, according to 
the atomic method, operating by way of substitution of atom 
for atom, foresee in certain cases the number of practicable 
substitutions. Thus, marsh-gas (CH,) containing four atoms 
of hydrogen, we may substitute in it chlorine for hydrogen 


* From the Moniteur Scientifique of Dr. Quesneville, April 1879. 


428 Sir B. C. Brodie on the Caleulus 


four times and no more. Similarly in ammonia (NH;) three 
analogous substitutions are possible. Whence we have, for 
example, the three ammonia bases, methylamine, dimethyl- 
amine, trimethylamine. Again, in chloride of ammonium 
(NH, Cl) we may have four such substitutions; and extend- 
ing this principle, we are able to anticipate in numerous cases 
the precise number of similar derivatives. All this, it is as- 
serted, is the work of the atomic method. Now the theory 
before us, says M. Naquet, does nothing of the kind, and, 

indeed, is incapable of doing it. We have ax, as the symbol 
of chloroform, and a’xy* as the tetrachloride of carbon. All 
that is here done to form the chlorine derivatives of marsh-gas 
is to add the weight y over and over again to the weight ax. 
Go on in the same direction, the next step brings youto ax’, 
an utterly impossible, or at least an eminently improbable, 
entity, which yet is not excluded from the system. 

The reply to this is that M. Naquet does not give a correct 
account of the process by which these derivatives are con- 
structed. We cannot make «xy by the same process as that 
by which a’xxy*is manufactured. After a’«y* is placed an insur- 
mountable barrier to progress in this direction which he does 
not see. He can go so far, but no further. 

M. Naquet’s criticism is based on a distinction for which he 
certainly is not responsible, as it is made in every chemical 
treatise, which is necessitated by the material mode of treat- 
ment of the atomic theory, but which, in this Calculus, does 
not exist, namely the distinction between Addition and Sub- 
stitution of atoms. For us the two processes are merged in 
one. (Part II. Section III. (9).) 

Let us consider the equation which expresses the relation 
between the chloride of iodine and its constituents, 

ay? + aw? =2ayo, 
or 
ay” + aw’? —2ayo=0. 
This equation vanishes when y=. It may be written 
thus | 
a(yvy—w)(y—w)=0. 

In this event & is constant, and it occurs in two ways by the 
substitution of w for y, which substitution is expressed by the 
symbol (y—o), and we have :— 


Symbol of the unit of chlorine............... “XY, 
% ‘s chloride of iodine... aay, 
Be WOCMIO. -Socte sees Soiree aww, 


in which Se ait the relation of substitution connecting these 
units is apparent. 


of Chemical Operations. — 429 
Now taking the equation | 
at+ay’=a2y, 
a(x—1)(x~—1)=0, 


an event in which « is constant, and which occurs in two ways 


by the operation (y—1). 


we have similarly 


Reasoning as before, we have :— 


Symbol of the-unit of chlorine ............ ayy, 
r 34 hydrochloric acid.. ay1, 
3 hydr OYE veseeeeeees all. 


Now the a rmbol 1 which appears in the symbols of hydro- 
chloric acid and of hydrogen is not the symbol of any real 
weight, but is the symbol of an empty unit of space serving to 
mark the place where matter is not, but has been, and may be 
again. The explicit introduction of this symbol into the 
symbol of the unit of hydrogen limits the number of the ope- 
rations x (or of any operation which may be substituted for y) 
which may be performed upon a, the unit of hydrogen, to 
two. Thus the operations w or 8 (which may be substituted 
for vy) may be performed once and twice upon the unit of 
hydrogen, but no more. Hence we have :— 

Symbol of the unit of hydrogen............ all, 
- Fe hydriodic acid...... awl, 
5 $9 Ladume eA Mewes os AWW ; 
but we have no means of making ao®, 

Now in the symbol e’«, the symbol of the two combined 
units of hydrogen, which (regarded purely . as the symbol of 
the weight of the combined hydrogen) is a’, becomes, by the 
explicit introduction of the symbol 1, o (1, ‘t 1; 1); and the 
symbol of marsh-gas is «’« (1, 1, 1, iL). In this case four 
successive substitutions of y for 1 are possible, by which the 
following units are constructed :— 


a "«(x; 1, , 1D 

a 216( Pel 

e eX, xX x; 1), 

a? K(X; XX x)» 
which are the symbols of the four chlorine derivatives of 
marsh-gas. But we have no means of constructing the unit 
oxy. (Part II. Section III. ( 12). ) 

Again, the unit of nitrogen av’ is derived from the unit of 
hydrogen by the substitution of v for 1 in that unit; and we 
have :— a(1,1) hydrogen, ~ 

a(v, 1) (anknown), 
a(v, v) nitrogen. 


Phil. Mag. 8. 5. Vol. 7. No. 45. June 1879. 2K 


430 Sir B. ©. Brodie on the Caleulus 


Effecting this substitution not in one but in two combined 
units of hydrogen, we have :— 

Symbol of two combined units of hydrogen .@? (1, 1, 1, 19, 

Symbol of the unit of ammonia .........00 a 2Cy, i 1, sole 


It hence appears that we can effect in the unit of ammonia 


three substitutions of y (or of any value of y) for 1, but no 
more. Now ex is the symbol of such a value of y, a fact as- 
certained by repeated experiments; and the symbols of these 
three derivatives are :— 

ot Vek, i ee ae 

ot Wake, ae, ile 

a'v(ak, ak, ak) $ 
hence the equation 

Bo KO + ov = 30M + KY 
expresses not only a result, but the final result of the action 
of iodide of methyl on ammonia. 
In the case of the chloride of ammonium, e’yv, putting 


aes te dw ld) 
as the symbol of three combined units of hydrogen, we have, 
effecting the substitution of y for 1 and of v for 1, 


axyv=a%(y,v, 1, 1,1, 1), 
in which four substitutions, and no more, of a« for 1 may be 
effected; whence we have 


a*(V, Vv, aK, aK, aK, aK) 


as the symbol of the unit of the chloride of tetra-methyl-am- 
monium. 

From the point of view of general algebra, al?=a, a’vl?=a’y, 
aK l*=a'K, a°*yvl*=a°*yv; we are therefore at liberty either 
to suppress the symbol 1 or to exhibit it according to our 
convenience. We may compare the symbol a’y (1, 1, 1) to 
an open fan, «vy to the same fan folded up. I have said 
enough to clear up the difficulty of M. Naquet; and this is 
not the place to further pursue the subject. 

With reference to the problem of the expression of “ Iso- 
mers ’”’ on the principles of the Calculus, I will venture to ask 
M. Naquet and others to suspend their judgment for a time™. 


It is a significant fact that a very large proportion of the 
class of elements which I have termed composite elements have 
not been found in the sun. In reply to inquiries on my part, 
Mr. W. Huggins writes to me thus :— 


* The following passage and also the footnotes have been added since 
the publication in the Moniteur Scientifique. 


of Chemical Operations. | 431 


“So far as I know, nitrogen, phosphorus, arsenic, antimony, 
boron, chlorine, iodine, bromine, have noé been found in the 
sun. In one paper Lockyer suspects iodine. Dr. Miller and 
I found coincidence of three lines of antimony with three lines 
in aldebaran. Though this observation would show conside- 
rable probability of antimony in star, I do not think the spec- 
troscope (two dense prisms of flint glass) was sufficiently 
powerful to make its existence there certain. In the case of 
nitrogen, no coincidence was observed in any of the stars. In ~ 
my paper in the Transactions of the Royal Society on Spectra 
of Nebulz, I show coincidence of principal line with the strong 
line in spectrum of nitrogen. Now this line of nitrogen is a 
double one; and I was not at first able to be certain if the line 
in the nebula was similarly double. Subsequently with the 
powerful spectroscope I used for the motions of stars, I was 
able to make a certain determination of this point (Proceedings 
R. 8. 1872, p. 385). I found the line in the nebula single and 
coincident with the middle of the less refrangible of the com- 
ponents of the double line 


Nitrogen. Red. 


Nebula. | 


I say “middle” because line in the nebula is narrower and more 
defined than either of the two lines forming the double line. 
I made experiments to see if under any conditions of pressure 
and temperature the more refrangible of the two lines fades 
out, so as to leave only the one with which the line in the 
nebula is coincident. I did not succeed. So the matter stands: 
—Is nitrogen compound? Are there any conditions under 
which the one line only appears? Has the line in the nebula 
no real connexion with nitrogen further than being sensibly 
of the same refrangibility ” ? : 

Now we must either consider that the matter of these ele- 
ments so abundant on the earth does not exist in the sun or 
stars (which is hardly probable), or that they have passed into 
forms of combination in which they cannot be recognized b 
the spectroscope (which is also hardly admissible at that ele- 
vated temperature), or that they have been decomposed. 


Second Note of M. A. Naquet. 


Sir B. C. Brodie replies victoriously to the principal objec- 
tion which we brought against him, and begs us to suspend 
our judgment on the second objection. We will therefore 
await the new memoir which his last sentence allows us to 
expect. 

2K 2 


432 Prof. G. Van der Mensbrugghe on a new Application 


There remain two objections to oppose to Sir B. C. Brodie; 
but they are of less importance. The first is that Sir B. C. 
Brodie admits, without any experimental proof, the compound 
nature of certain bodies considered simple, like chlorine and 
potassium, while others, like mercury, remain simple—although 
it appears, according to the law of Dulong and Petit, that all 
our elements ought to be compound, or none of them ought 
to be compound, at least of those to which the law of Dulong 
and Petit is applicable. We repeat, however, that though 
Lockyer’s experiences do not conclusively establish the com- 
pound nature of our elements, this would be one step towards 
the verification of Sir B. C. Brodie’s hypothesis. 

The second objection is that the law of even numbers, which 
serves as the basis of the new notation, can be thoroughly 
established in the series of carbon combinations, but it cannot 
be so completely established in the other series. It would 
perhaps be simpler to admit that this law is not universal 
than to admit that chlorine and nitrogen are compound bodies. 
In any case we cannot do better than repeat, in conclusion, 
that which we have already said. All hypotheses are but 
mental artifices to guide us to the discovery of truth; and 
since a new hypothesis opens new horizons to the investigator, 
this hypothesis may be fruitful, and ought to be accepted, 
either by replacing an old hypothesis which has become ste- 
rile, or by concurrence with it. It is for this reason that we 
have translated Sir B. C. Brodie’s memoirs; it is for this 
reason that we do not understand indifference towards his 
work, and that we should understand such indifference still 
less now that he has done away with one of the two principal 
difficulties which we thought we had found in ‘his system, and 
that he promises before long to do away with the second. 


LXVI. Onanew Application of the Potential Energy of Liquid 
Surfaces. By Professor G. VAN DER MENSBRUGGHE*. 


N arecent memoirt I sought to confirm my theory of the 
variations of potential energy of liquid surfaces by pre- 
senting a series of proofs drawn from the observation of liquid 
films either with two free faces or spread upon another liquid. 
I had hardly finished the writing of that memoir when my 
attention was drawn to the remarkable phenomena presented 


* Translated from a separate impression communicated by the Author, 
from the Bulletins de 1 AcadémieRoyale de Belgique, 2° série, t. xlvi.no. 11, 
STS. 

T “ Ktudes sur les variations d’energie potentielle des surfaces liquides,” 
Mém, de ? Acad. royale de Belgique, 1878, t. xliii. 


of the Potential Energy of Liquid Surfaces. 433 


by the plane or curved sheets of liquid first described by Sa- 
vart*, and afterwards studied by Hagen}, Tyndall{, Magnus, 
and Boussinesq||. I quickly recognized some very interesting 
verifications of my theory in the curious peculiarities mani- 
fested by those sheets, of which no satisfactory explanation 
has, to my knowledge, been yet furnished. In order to be 
able to continue without hurry the experimental control of 
my theoretic deductions, I will briefly explain how the prin- 
ciples of thermodynamics account for the effects in question. 

2. It is known from Savart’s observations that, if two veins 
of water with equal circular sections are impelled with equal 
and opposite velocities, and meet so that their axes coincide, 
there is formed, for all pressures sufficiently strong, a plane 
circular sheet bounded by a rough, agitated, and sonorous 
zone when the pressure exceeds a certain amount, but which 
for a less charge becomes perfectly smooth and even through- 
out its extent. From this it follows that, under favourable 
conditions, not merely the vis viva of the water after the im- 
pact of the two veins, but also the effects of gravity are almost 
completely nullified after a relatively very short course. What 
can be the cause that destroys so considerable an energy of 
motion? and by what is the latter replaced ? 

3. Since 1849 M. Hagen has invoked, as being that cause, 
the superficial tension of the liquid, which, having constantly 
to be overcome, gives rise to a retarding force. 

Doubtless the theory of M. Hagen is very ingenious, espe- 
cially for the time when it was sent forth ; but, besides that it 
does not clearly show the force which is substituted for the 
vis viva in proportion as this is destroyed, it does not make 
intelligible the various effects ascertained by Savart, except 
by means of an indispensable complement or, rather, a rectifi- 
cation. In the actual case the principle of the conservation of 
energy is verified, owing to the circumstance that the energy 
of motion of the two veins is almost entirely replaced by the 
potential energy of the superficial layers of the two faces of 


* “Mémoire sur la choc d’une veine liquide lancée contre un plan cir- 
culaire,” Ann. de Chim. et de Phys. de Paris, 1835, t. liv. p. 55; “Mémoire 
sur le choc de deux veines animées de mouvements directement opposés,” 
bid. t. lv. p. 257. 

+ “Ueber die Scheiben, welche sich beim Zusammenstossen von zwei 
Wasserstrahlen bilden, und tiber die Auflésung einzelner Wasserstrahlen 
in Tropfen,” Pogg. Ann. 1849, vol. lxvii. p. 451. 

ft On some Phenomena connected with the Motion of Liquids,” Phil. 
Mae. 1854, ser. 4, vol. vill. p. 74. 

§ “Hydraulische Untersuchungen,” Pogg. Ann. 1855, vol. xev. p. 1. 

|| Théorie des expériences de Savart sur la forme que prend une veine 
liquide aprés s’étre choquée contre un plan circulaire,’ Comptes Rendus, 
1869, t. [xix. pp. 45, 128. 


434 Prof. G. Van der Mensbrugghe on a new Application 


the sheet. On the other hand, the principles of thermody- 
namics require that the kinetic energy shall diminish, not only 
because the concentric rings widen, but moreover because, 
- precisely on account of the superficial enlargement on the two 
faces, the tension and with it the retarding force are more and 
more augmented. This last point follows as a consequence 
from my deductions already confirmed by a former series of 
experiments, which are described in my recent memoir. 

4, Applying my theory to Savart’s plane films, I arrived at 
the following results :— 

(a) The retarding force due to the augmentation of poten- 
tial energy goes on increasing in proportion as the liquid 
travelling over the disk removes further from the axis. 


(6) As we have c= < nearly, « being the thickness of the 


film at any point, C a constant, v the velocity at that point, r 
the distance from the axis, we conclude that, starting from 
the axis, e continually diminishes, since 7 increases more ra- 
pidly than v lessens. This gradual diminution of e will cease 
when vr no longer sensibly changes ; but soon the velocity 
decreases faster than r increases, and from that time the thick- 
ness must go on increasing by degrees until it attains a 
maximum. 

(c) When the velocity shall have become sufficiently reduced, 
e may pass through a series of maxima and minima, so that 
there will be formed, for sufficiently strong pressures, a series 
of circular waves joined to one another by eross striee, which 
will give rise to the production of minute drops, taking away 
from the outermost zone its transparence and its regularity of 
form. 

(d) If the velocity of the liquid, after the ‘impact, increases 
in a certain ratio, the retarding force increases in a greater 
ratio—which explains the remarkable fact that the liquid disks 
may become less in diameter when the charge is increased. 

These theoretic results are verified in all points by the ex- 
periments of the French physicist, and by the measurements 
furnished by them to M. Hagen. 

5. If my theory is susceptible of useful applications in the 
study of plane liquid sheets, it finds still. more curious appli- 
cations in relation to curved ones. According to Savart, such 

a sheet is obtained, for instance, by letting a liquid vein, shot 
thr ough an orifice of 12 millims., under a sufficient pressure, 
fall upon the centre of a horizontal brass disk fixed at the dis- 
tance of 20 millims. beneath. After impact the liquid spreads 
out in all azimuths, and gives rise to a curved film bounded 
by an indented margin. For a pressure of 2 metres the 


of the Potential Energy of Liquid Surfaces. 435 


sheet is thin, even, and transparent in its central part, and 
presents towards its contour the aspect of an annular zone 
or aureola covered with numerous circular striz connected 
by radial ones. In proportion as the charge is lessened the 
diameter of the sheet increases, the aureola becomes more 
transparent, narrower, and entirely disappears when the pres- 
sure at the orifice does not exceed 60 centims. The sheet then 
attains its maximum diameter (80 centims.), and affects the 
form of a wide cap, the concavity of which is turned down- 
wards. | 

To the whole of these phenomena the propositions enun- 
ciated at no. 4 are applicable. 

In proportion as the charge decreases, the sheet gradually 
becomes less in diameter, and at the same time curves back 
upon itself at its lower part, going toward the stem that sus- 
tains the disk; at a pressure of about 32 centims. the sheet 
closes up entirely, assuming the form of a solid of revolution 
with a perfectly even surface. . 

The formation of the closed figure is due, as has already 
been pointed out by M. Plateau, to the effect of capillary 
pressures in the lower portion of the sheet. 

6. We now come to the truly singular transformations ob- 
served by Savart. 

Directly after the closing of the sheet its dimensions dimi- 
nish, at first gradually, simultaneously with the charge ; when 
this no longer exceeds 10 centims. the shape of the sheet 
abruptly changes: the upper part suddenly becomes concave, 
rising above the plane of the disk; then, after an extremely 
short time, the former shape reappears; and these instanta- 
neous changes of aspect are periodically repeated seven or 
eight times, until the sheet entirely vanishes. 

Savart, who most carefully studied these abrupt changes, 
vainly endeavoured to penetrate the cause of them. Since 
then M. Boussinesq has essayed to give the mathematical 
theory of the formation of the even and closed sheets ; but, 
like M. Hagen, he regards the capillary constant as remaining 
the same in every part of the surface. His calculations, too, 
are not in accordance with experiment, and do not exhibit the 
cause of the instability of the sheets under certain conditions. 

The following are the propositions to which my theory has 
conducted me, and which, for the most part, I have verified 
by direct observation: — 

(a) To every quantity of energy of motion destroyed cor- 
responds necessarily, as in the case of the plane sheets, an 
equivalent amount of potential energy, the seat of which is 
the whole of both faces of the upper portion of the sheet, 


436 On the Potential Energy of Liquid Surfaces. 


limited at the equatorial section (I thus name the section the 
plane of which passes through the points where the tangent 
to the generatrix is vertical). 

I have, in fact, ascertained that, if the operation is conducted 
with a constant charge, there is never any sudden rising fol- 
lowed by the formation of a surface concave upwards ; no 
more is there such when the charge, instead of diminishing, 
goes on increasing; and, finally, there is none when, from any 
cause whatever, the sheet presents an aperture. 

(6) While the gradual development of potential energy in 
the upper portion of the sheet gives rise to a retarding force, 
there is developed, on the contrary, in the lower portion an 
accelerating force, due not merely to gravity, but also to the 
diminution of the potential energy of the liquid rings, which 
are incessantly narrowing right to the axis. It is owing to 
the increase of the velocity of the liquid that the water-threads, 
after encountering the axis, scatter in little drops. A Savart 
closed sheet thus presents a striking example of the transfor- 
mation of kinetic into potential energy, and of potential energy 
into energy of motion. 

(c) If while the sheet is closed the kinetic energy diminishes, 
either gradually or abruptly, the retarding force arising from 
the increase of potential energy in the upper part increases, 
either continuously or suddenly, and then struggles against 
the accelerating force that animates the lower part of the sheet. 
For this reason the film is strongly stretched: there is some- 
times delineated a projecting ridge; and immediately after- 
wards the sheet rises, becoming concave upwards; but then 
the retarding force which dominates the concave portion is 
directed downward, like gravity and the accelerating force of 
the lower part—which immediately brings back the sheet to 
its primitive form, but with smaller dimensions. 

While Savart generally operated only with charges decreas- 
ing in a continuous manner, I have verified the preceding 
theoretic consequence by abruptly diminishing the charge 10 
centims. I thus saw, after a few seconds, the singular figure, 
concave upward, formed which so much preoccupied the 
French physicist. , 

(d) According to my formula 

dT 
dQ=atd (8S), 


which gives the variation of heat dQ corresponding to an in- 
erement dS of the surface S, having the potential energy T, 
and absolute temperature ¢, the variation dQ must vanish with 


On the Detached Colorimeter. 437 


the differential coefficient | and in that case the potential 


energy T of the liquid does change ; consequently the retard- 
ing force in question above is not augmented then, as in the 
general case ; and for this reason the diameter of the sheet 
must be greater than usual. 

This curious result of my theory is fully confirmed by Sa- 
vart’s experiments. Withan orifice of 3 millims. the aureoled 
open sheet had a diameter of 20 centims. when the water was 
at 1°°3 C. and was impelled by the pressure of 4°885 metres ; 
while the sheet under the same pressure, but at the tempera- 
ture of 4° C., had a diameter of 36 centims.—that is to say, 
nearly four times the surface. In my opinion, this consider- 
able difference simply proceeds from the potential energy T of 
the water at its maximum of density having a maximum value, 


dT 
so that deco 


(e) If the foregoing conclusion is accurate, in operating 
with water at 10° C., for example, a cooling must be found to 
take place in the sheet, while, on the contrary, if the water is 
at first at, say, 1°3, it must grow warmer in spreading. 

(7) Since, as I have proved in a previous investigation, to 
every thermal variation a difference of electric potential cor- 
responds, the spreading-out of water at its maximum of density 
into a sheet cannot give rise to a thermoelectric current, pro- 
vided the temperature in it does not change ; on the contrary, 
the formation of the quid sheet must be accompanied by a 
current in one direction if the initial temperature of the liquid 
be above 4°'5, and in the opposite direction if it be below 4°°5. 

I purpose soon to control this important consequence of my 
formula. If direct observation verify it, I shall therein find 
a brilliant confirmation of the theory I am seeking to introduce 
into science. 


LXVII. On the Detached Colorimeter, and on Colorimetry. 
By Evuunp J. Mitts, D.Sc., F.R.S., “Young” Professor — 
of Technical Chemistry in Anderson’s College, Glasgow*. 


HE ordinary detached colorimeter consists of two equal 
test-tubes mounted on feet. It is a simple, but in many 
respects an imperfect, instrument. Several of its defects were 
removed by the Portable Colorimeter}, which has been found 
to work well in the majority of cases. Room, however, has 


* Communicated by the Author. 
t Proc. Phil. Soc. Glasgow, x. p. 310, 


438 Dr. EH. J. Mills on the Detached Colorimeter, 


still been left for an apparatus from which leakage at the bot- _ 
tom is impossible, and in which, as in the common detached 
colorimeter, the liquid comes into contact only with glass. 

The new detached colorimeter* is . 
made in two pieces, alike in every re- 
spect ; one of these is represented in the 
subjoined figure:—It consists of a stout 
glass tube having a broad flat foot, and 
graduated into 100 equal parts; its 
capacity at the upper part is about 120 
cubic centims. On the top of this is a 
loosely fitting brass cap, prolonged down- 
wards so as to cover and shade the sur- 
face of the liquid, thereby preventing the 
appearance of a dark meniscus. The 
surface of the liquid is only visible side- 
ways through the little aperture a, cut 
out for that purpose. ‘The cap is perfo- 
rated centrally; and a short tube ¢ rises 
from the perforation. ‘This tube is sol- 
dered laterally to a narrower one ?’, and 
this again to a small block b, from which 
rises a spring carrying another small 
block 6’. The tube ¢’ has, cemented into 
it, a glass tube u, which passes straight 
downwards, and reappears below the flat 
surface of the cap, its end amply clear- 
ing that surface. This tube is coned 
outwards at its upper extremity, but is 
left plain below. Through it there passes, 
with just sufficient room to move, the 
rod rv, bent below twice at right angles, 
so as to carry a flat circular “ opal” glass disk, to which it is 
attached by fusion. ‘These disks are turned in the lathe: their 
surfaces should be polished free from scratches, and their edges 
show no bevel. ‘The rod is prevented from falling by the easy 
pressure of the little half-tube A, carried by the block 6’. When 
the thumb and fore finger are lightly pressed on # and a’, the 
rod can be readily moved up and down, and will then stay in 
any position in which it may have been left. It is convenient. 
to cone outwards the half-tube h at both its ends; but only. 
traces of liquid ever reach this spot. 

The instrument has two accessories which are of consider- 
able service. These consist (1) of a pair of glass disks, d, 


* The instrument has been made for me by Messrs. Cetti and Co., 
Brooke Street, Holborn, 


and on Colorimetry. 439 


lying at the bottom of the tube, one having a suitable red, the 
other a green colour ; there is thus obtained a black ground, 
on which the opal disk is always seen through¢. Anannulus 
of deeper tint than a given observed colour would otherwise 
surround the opal disk, and tend to confuse the determination. 
Ii is an advantage at times to use other colours, and even to 
cover the opal disk with a plate of coloured glass. The other 
accessory is (2) a black hemispherical button n. This lies 
loosely on the opal disk, as shown in the figure. It is used in 
the estimation of turbidities (7. e. precipitates), by lowering it 
until its point just disappears. 

In taking readings, the position of the flat surface with 
regard to the scale is always the object to be ascertained; and 
this can be done, as is the case with Hrdmann’s float, so as 
entirely to avoid parallax. The level of the liquid’s surtace is 
afterwards taken; and the difference between the two readings 
is the depth required ; but if the button be used, the height 
of the button must be subtracted from that difference. 

It is of course obvious that any upward or downward move- 
ment of the rod must alter somewhat the level of the surface 
of the liquid. For small variations thus produced (as, for 
example, by a depression of two or three divisions) no correc- 
tion need be made. For larger variations, a factor is easily 
found by experiment ; it is probably the same in every speci- 
men of the instrument, viz. nearly 0-015 division for every 
division the rod is moved. This correction is perhaps rather 
better than direct reading. 


Remarks on Colorimetry. 


The colorimeter has been of late years more extensively 
used than formerly; but it would probably be much more 
widely employed if its service were better understood. ‘Thus, 
for example, a red liquid like a solution of magenta is admi- 
rably suited for colorimetric measurement, it having a tint to 
which the eye readily adapts itself. On the other hand, it is 
rare to find any one who can accurately estimate yellow. 
Something thus depends on the eye, and on the employment 
of the same eye. It must also be borne in mind that very few 
liquids will stand a dilution of over 20 per cent. without un- 
dergoing chemical change. Thus, a very weak solution of 
magenta differs in actual colour from a strong one. Hence it 
is obviously necessary to use the first determination as a mere 
approximation ; and, on that as a basis, to alter the strengths 
of the standard and trial liquid to equality. A second deter- 
mination is now made, and a still closer approximation obtained 


440 Dr. EH. J. Mills on Colorimetry. 


by its means—this process being repeated until there is only 
a difference of a division or two between the two liquids. 

The second approximation will in general be found suffici- 
ently exact. All dilutions should as far as possible have the 
same age. With regard to the standard tint selected, the ope- 
rator has in this colorimeter the means of varying his standard 
to any extent by shifting one opal disk ; he can thus work at 
the particular depth of tint which he finds most suitable to his 
own eye. Steady accuracy in any particular measurement 
can generally be obtained by at most a few days’ practice. 

Turbidities—In connexion with the Portable Colorimeter, 
I pointed out* that a black or coloured disk, lowered through 
a turbid liquid, eventually vanishes, and that the depth at 
which disappearance takes place is a measure of the amount 
of turbidity present. In this way, for example, it is easy to 
estimate the amount of water added to milk. It is obvious, 
however, that this method admits of quantitative extension to 
all sorts of precipitates, provided we can find a suitable medium 
‘to ensure their.suspension as a turbidity, and not in the ag- 
gregated state, during a s_itable time. 

The suspensory liquid I now employ consists of 100 grms. 
of gelatine, 100 grms. at most of glacial acetate (“acetic 
acid’’), and 1 grm. of salicylate (“salicylic acid’’) dissolved 
‘in a litre of distilled water: this is clarified with a little 
white of egg, and filtered hot. It remains permanently liquid 
in the cold, and does not putrefy. It may, if desired, be 
charged with any special reagent (baric chloride for instance): 
a volume of the mixture can then be added to a volume of a 
very weak standard sulphate, and also to a volume of sulphate 
of unknown strength ; by depressing the black buttons, the 
colorimeters determine the relation between the two. The 
reacting bodies should in such cases be the same; thus, hydric 
sulphate should not be compared against potassic sulphate. 
The key to success in colorimetry is, in fact, equality of con- 
dition. 

If the precipitant should be alkaline, or an alkalime carbo- 
‘nate, the gelatine solution should first be neutralized and then 
mixed with more alkali or carbonate. Such solutions as 
aqueous magnesic chloride and zine sulphate can then be 
-added, the whole instantly well shaken, and the result com- 
pared with a standard effect in the other tube. 

Lime can be determined by adding ammonia and ammonic 
oxalate to the suspensory liquid, and then a weak solution of 
ealcic salt. 

There is probably no substance incapable of suspension for 

* Loe. cit. p. 312. 


Geological Society. | — 441 


more than half an hour—a period sufficient for thirty compa- 
risons ; and most precipitates will refuse to fall for hours, 
sometimes for days, together. ‘Traces of argentic chloride 
will remain unprecipitated in this liquid for months. The 
operator has therefore only to select such a strength of 
standard precipitate as shall give him not too great an amount. 
to suspend, and an opacity equal to about fifty scale-divisions. 
If the substance precipitated should be soluble in the solution 
of gelatine, that solution should be saturated, before use, with 
the precipitate in question, 

The estimation of turbidities will doubtless prove of much 
value in water-analysis, in field work, in the valuation of 
pharmaceutical extracts precipitable by water (hitherto an un- 
approachable subject), in watching the variations in composi- 
tion of well-water for brewing-purposes, in the systematic 
examination of the atmosphere’s impurities, in Hggertz’s car- 
bon process, and in many similar lines of research. 

The colorimeter is an instrument admirably adapted for use 
in comparatively unskilled hands, and especially in those in- 
dustrial analyses where one class of product is constantly 
tested by asingle person. 


LXVIII. Proceedings of Learned Societies. 
GEOLOGICAL SOCIETY. 
‘ [Continued from p. 370. ] 
April 30.—Henry Clifton Sorby, Esq., F.R.S., President, in the 


Chair. 


a following communications were read :— 
1. “A Contribution to the History of Mineral Veins.” By 
John Arthur Phillips, Esq., F.G.S. ie 
In this paper the author described the phenomena of the depo- 
sition of minerals from the water and steam of hot springs, as illus- 
trated in the Californian region, referring especially to a great 
‘< sulphur bank” in Lake County, to the steamboat springs in the 
State of Nevada, and to the great Comstock lode. He noticed the 
formation of deposits of silica, both amorphous and crystalline, en- 
closing other minerals, especially cinnabar and gold, and in some 
cases forming true mineral veins. The crystalline silica formed 
contains liquid-cavities, and exhibits the usual characteristics of or- 
dinary quartz. In the great Comstock lode, which is worked for 
gold and silver, the mines have now reached a considerable depth, 
some as much as 2660 feet. The water in these mines was always 
at a rather high temperature ; but now in the deepest mines it issues 
at a temperature of 157° Fahr. It is estimated that at least 
4,200,000 tons of water are now annually pumped from the workings ; 


442 | Intelligence and Miscellaneous Articles. 


and the author discussed the probable source of this heat, which he 
was inclined to regard as a last trace of volcanic activity. 


2. “Vectisaurus valdensis, a New Wealden Dinosaur.” By J. 


W. Hulke, Esq., F.R.S., F.G.S. 


3. “On the Cudgegong Diamond-field, New South Wales.” By 
Norman Taylor, Esq., of the late Geological Survey of Victoria; 
communicated by R. Etheridge, Esq., Jun., F.G.S. 

The author described in detail the various spots at which dia- 
monds have been found in this locality. They occur in river-drift, 
associated with gold and other gems. The drifts in the district are 
at least six in number. The oldest is considered by the author to 
be Upper Miocene or Lower Pliocene; the next Middle Pliocene; 
others Upper Pliocene, Pleistocene, and Recent. Between the 
Middle and Upper Pliocene flows of basalt lava took place, which 
have sealed up much of the older drifts. Diamonds are found in the 
oldest drift and, probably by derivation from it, m the newer. 
Gold, metallic iron, wood, tin, brookite (?), iron-sand, quartz, tour- 
maline, garnet, pleonast, zircon, topaz, sapphire, ruby, and corun- 
dum are also found. The author then considers the question of 
whether the diamonds are derived from some of the igneous or 
sedimentary formations (from Upper Silurian to Mesozoic) which 
have contributed to the drift; and concludes, from a variety of 
reasons, that the diamonds have been formed in situ in the older 
drift. 


4. “On the Occurrence of the Genus Dithyrocaris in the Lower 
Carboniferous, or Calciferous Sandstone Series of Scotland ; and on 
that of a second species of Anthrapalemon in these beds.” By R. 
Etheridge, Esq., Jun., F.G.S8. 


LXIX. Intelligence and Miscellaneous Articles. 
NOTE ON THE MAGNETIC EFFECT OF ELECTRIC CONVECTION. 


To the Editors of the Philosophical Magazine and Journal. 

Johns Hopkins University, 

GENTLEMEN, Baltimore, April 8, 1878. 
ents three years since, while in Berlin, I made some experi- 
ments on the magnetic effect of electric convection, which have 
since been published in the ‘ American Journal of Science’ for Ja- 
nuary 1878. But previous to that, in 1876, Professor Helmholtz 
had presented to the Berlm Academy an abstract of my paper, 
which has been widely translated into many languages. But, 
although Helmholtz distinctly says “Ich bemerke dabei, dass der- 
selbe den Plan fiir seme (Rowland’s) Versuche schon gefasst und 
volistandig iiberlegt hatte, als er in Berlin ankam, ohne vorausge- 
hende Einwirkung von meiner Seite,” yet nevertheless I now find 
that the experiment is being constantly referred to as Helmholtz’s 


eee 


Intelligence and Miscellaneous Articles. 448 


experiment—and that if I get any credit for it whatever, it is 
merely in the way of carrying out Helmholtz’s ideas, instead of all 
the credit for ideas, design of apparatus, the carrying out of the 
experiment, the calculation of results, and every thing which gives 
the experiment its value. 

Unfortunately for me, Helmholtz had already experimented on 
the subject with negative results ; and I found, in travelling through 
Germany, that others had done the same. The idea occurred in 
nearly the same form to me eleven years ago; but as I recognized 
that the experiment would be an extremely delicate one, I did not 
attempt it until I could have every facility, which Helmholtz kindly 
gave me. 

Helmholtz kindly suggested a more simple form of commutator 
than I was about to use, and also that I should extend my experi- 
ments so as to include an uncoated glass disk as well as my. gilded 
vulcanite ones ; but all else I claum as my own, the method of expert- 
ment in all its details, the laboratory work, the method of calculation— 
endeed every thing connected with the experiment in any way, as com- 
pletely as if it had been carried out in my own laboratory 4000 miles 
from the Berlin laboratory. 

3 Yours truly, 
H. A. Rownanp. 


ON ELECTRIC BOUNDARY LAYERS. BY PROF. HELMHOLTZ. 


In all cases in which two contiguous bodies have different values 
of the electric-potential function, there must be along the common 
boundary between them a double layer of positive and negative 
electricity, the moment of which (taking this expression in the 
same sense as in the phrase ‘magnetic moment”), multiplied by 
47, calculated for unit surface, is equal to the difference of poten- 
tial-function on the one side and on the other of the double layer. 
Now, as the value of the moment is equal to the electric density of 
the positive E multiplied by the mean value of the distance between 
the two layers, this distance cannot become vanishingly small with- 
out the density with a given difference of potential becoming infi- 
nitely great. But the work done, in the formation of such a double 
layer, against the electrostatic forces is =PE, if E denotes the 
amount of positive electricity on the unit of surface, and P the dif- 
ference of potential on the two sides of the double layer. Since, 
with the distance h between the two layers, 


4rEh=P, 
the value of the work is 
1 
Si oy eee 2 
2 ou Srh 3 fi 


and would therefore become infinite for vanishing #. From this 
Sir William Thomson has already calculated a limit for the distance 
between the double layer at the galvanic tension between copper 


444 Intelligence and Miscellaneous Articles. 


and zine, according to which calculation it must be more than 
3 X 10-7 millim. With this agree F'. Kohlrausch’s experiments on 
the capacity of galvanically polarized platinum surfaces for very 
weak charges, from which the distance comes out equal to the 
2475000th part of a millimetre, if the potential-difference be as- 
sumed to be equally divided between the two plates. 

The author showed that the laws of the flow of water through 
capillary tubes and porous diaphragms occasioned by electric cur- 
rents, as ascertained by G. Wiedemann and Quincke, and the laws 
of the electric tension excited by the flowing of water, between the 


beginning and the end of the course of the stream, discovered by 


the latter observer, can all be deduced from the hypothesis that a 
difference of electrical potential exists between the sides of the 
vessel and the liquid (which M. Quincke also assumed, and sup- 
ported by many experiments), and that it is the part of the double 
layer falling in the water that both yields to the electric attractive 
forces on the tube being traversed by an electric current, and is also 
taken along by the introduced motion of the water, The boundary 
layer of the liquid must be assumed to be at rest against the sides 
of the tube, as in Poisseuille’s theory of the flow of liquids in capil- 
lary tubes. In a series of cases the data supplied suffice for the 
calculation of the electric moment of the part of the double layer 
that falls in the liquid (in which calculation the opposite electricities 
must be assumed to be combined in the bounding surface). The 
values then obtained do not exceed those with which we are ac- 
quainted from the galvanic tensions between metals. 

Thus M. Wiedemann’s experiments on the electric conveyance of 
sulphate-of-copper solution through clay diaphragms give the mo- 
ment of the electrical layer in the liquid as equal to 2°4 Daniells. 
M. Quincke’s experiments on the height to which water, conveyed 
by electricity, ascends in glass tubes give 3:9 Daniell’s; and his 
experiments on the electric tensions which arise when very dilute 
salt-solutions are driven through clay diaphragms give 1:9-2-7 
Daniells. As the electromotive force between potassium and pla- 
tinum amounts to about 3°4 Daniells, all the above-mentioned 
numbers lie within or but little beyond the limits of the observed 
differences of potential between metals. 

The assumption that the extreme boundary layer of the liquid 
adheres immovable to the sides of the vessel was founded upon the 
determinations made by M. Quincke of the heights of ascent of 
electrically carried liquid in cylindrical glass tubes, according to 
which they are inversely proportional to the square of the radius. 
This results from the theory only on the assumption that no sliding 
of the boundary layer occurs. The calculation was accomplished 
even for those cases in which a cylindrical thread is placed in a cy- 
lindrical tube ; and it showed tolerable accordance with the obser- 
vations, so far as could be expected with experiments so subtile and 
so disturbed by manifold influences.—Monatsbericht der kon. preuss. 
Akadenve zu Berlin, Feb. 1879, pp. 98-200. 


Intelligence and Miscellaneous Articles. 445 


A THEORETIC AND EXPERIMENTAL DEMONSTRATION OF THE DE- 
FINITION, “ THE TEMPERATURE OF A BODY IS REPRESENTED 
BY THE LENGTH OF THE THERMAL OSCILLATION OF ITS MO- 
LECULES.”’ BY R. PICTET. 


If we admit that heat is only the manifestation pure and simple 
of the molecular forces with which the constituent particles of 
bodies are endowed, we must necessarily admit also that the me- 
chanical work taken up by the thermal motion must displace the 
particles from their position of equilibrium and make them move in 
trajectories of an elliptic form, the amplitude of which will be pro- 
portional to the work consumed. 

At absolute zero there is no oscillation, the cohesion is maximum ; 
at a certain temperature, fixed for each body, the oscillation will 
be maximum, and the body, being disaggregated, will dissolve; the 
molecules will be sufficiently apart to be out of the conditions of 
stable equilibrium. 

In this hypothesis absolute contact of material particles is ren- 
dered impossible by the action of the ether; for we admit that the 
attraction of matter for the ether does not follow the same law as 
the attraction of matter for matter: for short distances the attrac- 
tion of matter for the ether prevails over the attraction of matter 
for itself. 

Under these conditions the repulsive forces are useless ; there 
would exist in nature only attractive forces. 

On these bases let us consider the action produced by external 
work supplied to a body supposed at absolute zero. Each molecule 
will begin to vibrate and oscillate from an extreme exterior position ~ 
to another position, an interior limit. The evident result of this 
molecular motion will be to increase the volume of the body in 
proportion to the mean length of the oscillations of its elementary 
particles. 

The coefficient of dilatation will therefore be in accordance either 
with the number of molecules contained in the body, or with the 
volume in which those molecules are contained, or, lastly, with the 
physical forces involved in thermal motion. 

Now the two following postulates can be admitted :— 

The laws of the attraction of matter for matter are absolutely general 
and unwersal. 

The phenomena of the disaggregation of bodies are subject to those 
laws. 

These being admitted, let N be the number of molecules con- 
tained in unit length of a solid body, /’ and Z the lengths of oscilla-: 
tion corresponding to the temperatures ¢’ and ¢; let a be the coefli- 
cient of dilatation of the solid body. We shall evidently have the 


following equality :— 
{'sa =. adt 
Jt t 


Now N is defined by the density and atomic weight of the solid 
body. 


Phal. igh S. 5. Vol. 7. No. 45. June 1879. 2A 


446 Intelligence and Miscellaneous Articles. 


Ph Te : | 
- In 1 cubic metre there are = molecules, calling the density d, and 


the atomic weight ». If we wish to get the number of the mole- 
cules N (that is to say, the number of molecules contamed in the 
linear unit or the edge of the cube), we have 


Taking « for the measured lengthening between zero and 100° C., 
we get directly the relation 


100 0 a/ A 
P 3 

Such is the value of the augmentation of the thermal waye- 
length when the temperature passes from zero to 100°. 

Now, if the attraction of matter for matter obeys a general law, 
every solid molecule will divide into two or more liquid molecules 
when the oscillations have become equal to a certain maximum, 
constant for all bodies. 

We have therefore to verify two physical laws which are the ne- 
cessary consequence of these deductions :— 

Ist. The higher the fusion-temperature of a solid, the shorter must 
the molecular oscillations be. . 
2nd. As the fusion-temperatures of solids correspond to equal 
lengths of oscillation, the product of the osciliation-lengths into the 

fusion-temperatures must be a number constant for all solids. 

These two laws are verified with as much exactness as the expe- 
rimental determinations of the various elements entering into the 
equations permit. 

The following Table comprises the metals of which the coefficients 
of dilatation are known with sufficient accuracy :— 


Table of the Thermal Wave-lengths of Solids, and of the Product 
. of their Multiplication by the Fusion-temperatures*. 


Fusion- |P. rude 
Atomic | Densi- | Values of | Wave-  |tempera-| ¢x% z 


“ETE. weights. | ties. a. lengths. | tures. ii ; 
273°+ p 
Selenium ...| 39°75 4°30 | 0:00368 | 0:007725 217. | 3°7854 
(DYER Ts Rapa 104 11°35 | 0:0028657 | 0:005382 305 | 3:272 
PRTC eet eee 327 719 | 0:002942 | 0:004873 450 | 3:523 
Silver Gat. 54 10°60 | 0:00193 | 0:003077 977 | 33841 
Copper ...... 31°75 8:9 0001715 | 0:0026215| 1050 | 3-468 
Gold 28 2% 98 19-258 | 0-:001466 | 0:0025205| .1100 | 3-459 
i aka 01 PR ae 28 7-79 | 00011717 | 0:0017805; 1600 | 3:34 
Platinum ...| 98°5 21:53 | 0:0008842 | 0:001467 | 1700 | 3:59 


* The wave-lengths are in the inverse ratio of the fusion-temperatures ; 
and the products are sensibly constant. 


Intelligence and Miscellaneous Articles. 447 


We may therefore regard the two postulates above indicated as 
correct. 

The temperature is really represented by the length of oscillation _ 
of the molecules of solid bodies. 

Analogous equations connect the elements of volatile liquids 
when compared at their boiling-points.—Comptes Rendus de 0 Acu- 
démie des Sciences, April 28, 1879, t. Ixxxvill. pp. 855-857. 


ON OZONE AND THE ELECTRIC EFFLUVIUM. BY M. BERTHELOT. 


1. The following are some experiments selected from those which 
I have made in the course of my researches upon persulphuric and 
hyperoxygenated acids, experiments the results of which appeared 
to me worth making known. 

2. First, of the combination of oxygen with hydrogen. I have 
found that these two gases, mixed in the proportion of 2 volumes 
of hydrogen to 1 of oxygen, do not combine under the influence 
of the effluvium, even at the end of several hours, either in concen- 
tric sealed glass tubes*, or in a tube surrounded by a lamellar 
spiral of platinumT and placed over mercury; in my trials the 
tension was nearly that developed across air by sparks of 7 or 8 
centims. length in operating with an induction-coil furnished with 
a condenser. No doubt, by progressively increasing the tensions 
up to approximately those which produce disruptive discharges, 
the formation of water would be provoked. But it appeared to 
me of interest to prove that that formation does not take place 
with such tensions as the preceding, and'under conditions where 
the portion of ozone formed is very considerable. 

The resistance of hydrogen to combination under these conditions 
is the more remarkable, as they are precisely those under which 
oxygen combines with metals, with sulphurous acid, arsenious acid, 
iodine, and even with nitrogen, although this last reaction demands 
considerably stronger electrical tensions than the others. 

Under these conditions, moreover, the vapour of water is not 
decomposed by the effluvium, nor does oxygen combine with water 
to form oxygenated water. 

3. These phenomena contrast with those which I have observed 
on carbonic acid. In fact, the oxide of carbon and oxygen, mixed 
in a test-tube over mercury in the proportion of two volumes of 
the one to one volume of the other, combine under the influence 
of similar electric tensions to the preceding. After twelve hours 
there remained only 8 per cent. of oxide of carbon and 2 per cent. 
of oxygen. One part of the latter had been absorbed by the mer- 
cury ; and a portion (about 5 hundredths) of the oxide of carbon 
had co-operated in the formation of the brown suboxide, C, O,. 

This incompleteness of the reaction is not less manifest in the 


* Annales der Chinue et de Physique, 5 série, t. xi. p. 466. 
+ Tbid: tx. py 19: 


448 Intelligence and Miscellaneous Articles. 


presence of an excess of oxygen. For example, on mixing, over 
mercury, equal volumes of oxide of carbon and oxygen, 1 found 
after some hours 93 per cent. of the oxide of carbon changed into 
carbonic acid, 5 per cent. into suboxide, and 2 per cent. unaltered. 
There remained 42 per cent. of free oxygen, including a little ozone. 
The presence of an excess of oxygen, therefore, does not determine 
the total combination of the oxide of carbon. 

Reciprocally, it does not prevent incipient decomposition of 
carbonic acid, as I have specially ascertained. Nay, more: in a 
mixture of equal volumes of carbonic acid and oxygen I found, 
after twelve hours, in a system of two concentric tubes, 5 per cent 
of the gas decomposed into carbonic oxide and oxygen. This oxy- 
gen contained a strong dose of ozone (or of percarbonic acid). 

These results establish the existence of the two opposite reactions 
provoked by the effluvium, and consequently that of the chemical 
equilibria determined thereby ; but it has not been possible to extend 
them on both sides to the same limit, on account of the secondary 
reactions, such as the formation of the suboxide of carbon and the 
absorption of oxygen by mercury. 

4, The decomposition of carbonic acid by the effluvium, effected 
in a space free from mercury and oxidable substances, gives rise to 
special phenomena worthy of our interest ; for they lead one to 
suspect the existence of percarbonic acid. In fact, in an experi- 
ment, after twelve hours of the effluvium acting upon a gas enclosed 
in the annular space of the concentric tubes hermetically sealed 
which I am accustomed to employ, I found 16 hundredth parts of 
of carbonic acid decomposed. ‘The gas which was formed attacked 
mercury and oxidable bodies with extreme violence. 

If the oxidating portion of this gas were regarded as ozone, the 
quantity of that substance would amount to 30 per cent. of the 
oxygen liberated in one experiment, and up to 41 per cent. in an- 
other—enormous proportions, and much higher than those produced 
with pure oxygen*. 

It would be very interesting to isolate the oxidating material 
formed in this reaction; but when one essays to eliminate the 
carbonic acid and the oxide of carbon contained in the preceding 
mixture, the oxidating gas is destroyed by the reagents employed, 
which does not permit its isolation. This gas might be equally 
regarded either as oxygen very rich in ozone, or as containing a 
strong dose of percarbonic acid, C, O,; but I have not succeeded 
iu discovering any proper character to distinguish the latter com- 
pound from ozone mixed with carbonic acid.—Annales de Chimie 
et de Physique, May 1879, ser. 5, t. xvil. pp. 142-144. 


* These proportions are relative to the oxygen produced by the decom- 
position of carbonic acid—which oxygen formed’ on 8 hundredths of the 
volume of the whole mixture in one experiment, 5 hundredths in the 
other, 


F 

3 

s 

. 
2a 


i 449 


INDEX to VOL. VII. 


ABNEY (Capt. W. de W.) on the 
photographic method of registering 
absorption-spectra, 313. 

Acoustical observations, 149. 

Actinometry, on a new method in, 
393. 

Air, on the effect of the motion of 
the, within an auditorium upon its 
acoustic qualities, 111. 

Anthracene-blue, on the fluorescent 
properties of, 144. 

Aron (H.) on the theory of the mi- 
crophone, 377. 

Ayrton (Prof. W. E.) on the music 
of colour and visible motion, 117; 
on the ratio of the electromagnetic 
to the electrostatic unit of electric 
quantity, 277; ona new theory of 
terrestrial magnetism, 401. 

Baily (W.) on starch and unannealed 
glass under the polariscope, 39. 
Bayley (J.) on catalysis, and the no- 

menclature of oxides, 126. 

Beetz (Prof. W.) on the excitation 
of electricity at the contact of solids 
and gases, l. 

Berthelot (M.) on the part played by 
pressure in chemical phenomena; 
70; on the specific heats and heat 
of fusion of gallium, 75; on ozone 
and the electric effluvium, 447. 

Bichat (E.) on the magnetic rotatory 
power of vapours, 371. 

Bile, on the action of the, in diges- 
tion, 301. 

Binaural audition, on the theory of, 
181, 261. 

Bisulphobichloranthacenous acid, on 
the fluorescent properties of, 144. 

Blaikley (D. J.) on the correction to 
be added to the length of a cylin- 
drical resonant tube to find the true 
wave-length, 339. 

Blowpipe, on an electrical, 372. 


Books, new :—Blanford’s Indian Me- 
teorological Memoirs, 64; Pres- 
cott’s Speaking Telephone, 140; 
Draper’s Scientific Memoirs, 211; 
Selwyn’s Geological Survey of Ca- 
nada, 213; Clarke’s Sedimentary 
Formations of New South Wales, 
214; Rutley’s Text-book on Petro- 

- logy, 289; Terquem’s Courbes dues 
a la Combinaison de deux Mouve- 
ments vibratoires perpendiculaires, 
365; the American Journal of Ma- 
thematics, Vol. I., 366. 

Bouty (M.) on the pressures exerted 
by galvanic deposits, 378. 

Bouvet (A.) on electrochemical ac- 
tions under pressure, 148. 

Boys (C. V.) on a condenser of vari- 
able capacity, 108. 

Brodie (Sir B. C.) on the calculus of 
chemical operations, 427. 

Brough (R. 8.) on the proper relative 
sectional areas for copper and iron 
lightning-rods, 336. 

Brown (F. D.) on the maintenance of 
constant pressures and tempera- 
tures, 411. 

Brown (J.) on a theory of voltaic 
action, 109. 

Catalysis, on, 126. 

Chase (Dr. P. E.) on harmonic orbits, 
224; on a new estimate of sun’s 
distance, 377. 

Chemical operations, on the calculus 
of, 418, 

phenomena, on the part played 
by pressure in, 70. 

Colorimeter, on the detached, 437. 

Colour, on the music of, 117. 

Condenser, on a, of variable capacity, 
108. 

Cook (E. H.) on the existence of the 
luminiferous ether, 225. 

Cooper (W. J.) on the moist-eom- 


450 


bustion process, 138; on the pro- 
ducts of oxidation of wool, 356. 

Crookes (W.) on the illumination of 
lines of molecular pressure, and the 
trajectory of molecules, 57. 

Crookes’s force, on the mechanical 
theory of, 15, 179. 

Current-regulator, on an automatic, 
i. 

Cyano-propionic acid, on the prepa- 
ration and properties of, 356. 

Diffraction, on a new proposition in 
the theory of, 51. 

Digestion, on the action of the bile 
in, 301. 

Diopside rock, on an artificial, 133. 

Dufour (H.) on Bell’s telephone, 222. 

Duter (E.) on a new phenomenon of 
static electricity, 69. 

Electric boundary layers, on, 443. 

convection, on the magnetic 
effects of, 442, 

—— currents, on the transmission 
and distribution of energy by, 352; 
of great strength, on methods of 
measuring’, 165. 

effluvium, on the, 447. 

light, on the theory of the, 29. 

quantity, on a new determina- 
tion of the ratio of the electromag- 
netic to the electrostatic unit of, 
277. 

Electrical burner and blowpipe, on 
an, 372. 

resistances, on high, 162. 

Electricity, on the excitation of, at 
the contact of solids and gases, 1 ; 
on anew phenomenon of static, 69. 

Electrochemical actions under pres- 
sure, on, 148. 

Electromagnets in telegraphy, note 
on, 145. 

Emulsions, on the formation of, 301. 

Energy, on the dissipation of, 344; 
on the transmission and distribu- 
tion of, by the electric current, 352. 

Enstatite rock in South Africa, on 
the occurrence of a pure and mas- 
sive, 135. 

Kurope, on the physical state of Cen- 
tral, during the tertiary period, 72. 

Fisher (O.) on the thermal conditions 
and on the stratification of the ant- 
arctic ice, 381. 

Fitzgerald (G. F.) on the mechanical 
theory ot Crookes’s force, 15, 179; 
on the electromagnetic theory of 


INDEX. 


the reflection and refraction of 
light, 216. 

Flames, on pure tones from sound 
ing, 149. 

Fluorescent substances, on two new, 
144. ) 
Frohlich (J.) on a new proposition 

in the theory of diffraction, 51. 

Gallium, on the specific heats and 
heat of fusion of, 75. 

Galvanic deposits, on the pressures 
exerted by, 375. 

Galvanometer, on a new absolute, 
274. 

Gas batteries, on the seat of the elec- 
tromotive force in, 1. 

Gases, on the excitation of electricity 
at the contact of solids and, 1; on 
the spectra of mixed, 77, 90; or 
the luminosity of, through elec- 
trical discharges, 248; on the elec- 
trical luminous phenomena of ra- 
refied, 297. 

Geological Society, proceedings of 
the, 66, 142, 215, 291, 367, 441. 
Glacial erosion of lake-basins, on the 

theory of, 240. 

Glaisher (J. W. L.) on a property of 
vulgar fractions, 321. 

Glass, on the comportment of unan- 
nealed, under the polariscope, 39; 
on the electrical perforation of, 374. 

Goniometer, on a horizontal, 136. 

Harmonic orbits, on, 224. 

Heaviside (O.) on electromagnets in 
telegraphy, 143. 

Helmholtz (Prof.) on electric boun- 
dary layers, 443. 

Hennessy (Prof. H.) on the figure of 

. the planet Mars, 67. 

Hodges (N. D. C.) ona new absolute 
galvanometer, 274. 

Hopkinson (Dr. J.) on high electrical 

- resistances, 162. 

Hospitalier (M.) on an automatic 
current-regulator, 71. 

Ice, on the modulus of cohesion of, 
240; on the thermal conditions and 
on the stratification of the ant- 
arctic, 381. 

Todides, on the action of light upon 
the soluble, 393. : 

Jacques (W. W.) on the effect of the 
motion of the air within an audito- 
rlum upon its acoustic qualities, 
111; on the velocity of very loud 
sounds, 219. 


INDEX. . 


Jamin (M.) on an electrical burner — 


and blowpipe, 372. 

Kundt (A.) on the electromagnetic 
rotation of the plane of polarization 
of light in the vapour of sulphide 
of carbon, 173. 

Lang (V. von) on a horizontal gonio- 
meter, 126; on the optical proper- 
ties of starch, 370. 

Leeds (Dr. A. R.) on the action of 
light upon the soluble iodides, 393. 

Lewis (W. J.) on the analysis of the 
rhombohedral system, 176. 

Light, on the theory of the electric, 
29; on the electromagnetic rota- 
tion of the plane of polarization of, 
in the vapour of sulphide of carbon, 
173; on the electromagnetic theory 
of the reflection and refraction of, 
216; on the action of, upon the 
soluble iodides, 893. 

Lightning, on spectra of, 316. 

Lightning-rods, on the proper rela- 
tive sectional areas for copper and 
iron, 336. 

Liquids, on the diffusion of, 74, 295. 

Liquid surfaces, on anew application 
of the potential energy of, 482. 

Lodge (Dr. O. J.) on the determina- 
tion of the variation of the thermal 
conductivity of metals, 198, 251, 
380. 

Lommel (E.) on two new fluorescent 
substances, 144. 

Luminiferous ether, on the existence 
of the, 225. 

Magnetism, on a new theory of ter- 
restrial, 401. 

Magnets, on the morphological laws 
of the configurations formed by 
floating, 98. 

Mars, on the figure of the planet, 67. 

Maskelyne (N.8.) on the crystallo- 
graphy of the nitrosoterpenes, 129; 
on an artificial diopside rock, 133; 
oe enstatite rock from South Africa, 

35. 

Matter, on an ultra-gaseous state of, 
63. 

Mayer (A. M.) on the morphological 
laws of the configurations formed 
by floating magnets, 98. 


Mensbrugghe (Prof. G. van der) on 


a new application of the potential 
energy of liquid surfaces, 432. 
Metals, on the determination of the 


451 


variation of the thermal conducti- 
vity of, 198, 251, 380. 

Microphone, on the theory of the, 
B77. ; 

Mills (Prof. E. J.) on the detached 
colorimeter and on colorimetry, 

ov. 

Mineral veins, on the formation of, 
44], 

Molecular pressure, on the illumina- 
tion of lines of, 57. 

structure, on the explanation of 
some phenomena of, 98. 

Motion, on visible, 117. 

Naquet (A.) on Sir B. C. Brodie’s 
calculus of chemical operations, 418. 

Nitrosoterpenes, on the crystallogra- 
phy of the, 129. : 

Oldham (R. D.) on the modulus of 
cohesion of ice, 240. 

Oxides, on the nomenclature of, 126. 

Oxygen, on the spectrum of, 297. 

Ozone, observations on, 447, 

Paalzow (M.) on the spectrum of 
oxygen, and on the electrical lu- 
minous phenomena of rarefied 
gases, 297. 

Permanganate of potash, on some re- 
actions of alkaline, 138. 

Perry (Prof. J.) on the music of 
colour and visible motion, 117; on 
the ratio of the electromagnetic to 
the electrostatic unit of electric 
quantity, 277; on a new theory of 
terrestrial magnetism, 401. 

Phillips (J. A.) on mineral veins, 
44]. 


Photographic method of registering 
absorption-spectra, on the, 313. 
Pictet (R.) on a demonstration of the 
definition “the temperature of a 
body is represented by the length 
of the thermal oscillation of its 

molecules,” 445. 

Polariscope, on the behaviour of 
starch and unannealed glass under 
the, 39. 

pee (W. H.) on the electric light, 
2 


Pressure, on the part played by, in 
chemical phenomena, 70. 

Pressures, on the maintenance of con- 
stant, 411. 

Quincke (Dr. G.) on the formation 
of emulsions, and the action of the 
bile in digestion, 301. 


452 


Radiation, on thermal, at high tem- 
peratures, 145. 

Rayleigh (Lord), acoustical observa- 
tions by, 149. 

Reynolds (Prof. O.) on the mecha- 
nical theory of Crookes’s force, 179. 

Rhombohedral system, on the ana- 
lysis of the, 176. 

Rontgen (W. C.) on the electromag- 
netic rotation of the plane of pola- 
rization of light in the vapour of 
sulphide of carbon, 173. 

Rowland (Prof. H. A.) on the mag- 
netic effects of electric convection, 
442. 

Schuster (Dr. A.) on an easy method 
for adjusting the collimator of a 
spectroscope, 95; on spectra of 
lightning, 316. 

Siemens (Dr. C. W.) on the trans- 
mission and distribution of energy 
by the electric current, 352. 

Solar physics, on the application of 
the photographic method of regis- 
tering absorption-spectra to, 313. 

Soret (J. L.) on thermal radiation at 
high temperatures, 145. 

Sound, on the theory of, 181, 261; 
on the velocity of, in small tubes, 
339. 

Sounds, on the velocity of very loud, 
219. 

Spectra, on the nature of, 77, 248. 

of lightning, on, 316. 

Spectroscope, on an easy method of 
adjusting the collimator of a, 95. 

Spectrum of oxygen, on the, 297. 

Starch under the polariscope, on, 39; 
on the optical properties of, 370. 

Stefan (J.) on the diffusion of liquids, 
74, 295. 

Steinhauser (A.) on the theory of 
binaural audition, 181, 261. 


INDEX. 


Pe distance, new estimate of the, 
377. 
Tait (Prof. P. G.) on the dissipation 
of energy, 344. 
ew on electromagnets in, 
43. 


Telephone, on the inductions that 
occur in the, 34; researches on 
Bell’s, 222. 

Temperatures, on the maintenance of 
constant, 411. 

Thermal conductivity of metals, on 
the determination of the variation 
of the, 198, 251, 380. 

Thermodynamic motivity, on, 348. 

Thomson (Sir W.) on the dissipation 
of energy, 344; on thermodynamic 
motivity, 348. _ 

Trowbridge (Prof. J.) on methods of 
measuring electric currents of great 
strength, 165. — 

Van Tieghem (M.) on the physical 
state of Central Europe during the 
Tertiary period, 72. 

Vapours, on the magnetic rotatory 
power of, 371. 

Voltaic action, on the theory of, 109. 

Vulgar Fractions, on a property of, 
321. 

Waltenhofen (Prof. A. von) on the 
electrical perforation of glass, 374. 

Wanklyn (J. A.) on the moist-com- 
bustion process, 138; on the pro- 
ducts of oxidation of wool, 356. 

Weber (Prof. H. F.) on the induc- 
tions that occur in the telephone, 
34, 

Wiedemann (H.) on the nature of 
spectra, 77; on the luminosity of 
gases through electrical discharges, 
248. 


Wool, on the products of oxidation 
of, 356. 


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